Given: WS bisects
Grandmother, mother and daughter are celebrating 150 years of life. The Mother is 25 years older thaGrandmother, mother and daughter are celebrating 150 years of life. The Mother is 25 years older than her daughter, but 31 years younger than her mother (the grandmother). How old are the three
Let grandmother's age be g. Let mother's age be m. Let daughter's age be d. We're given 3 equations:
[LIST=1]
[*]m = d + 25
[*]m = g - 31
[*]d + g + m = 150
[/LIST]
This means the daughter is:
d = 25 + 31 = 56 years younger than her grandmother. So we have:
4. d = g - 56
Plugging in equation (2) and equation(4) into equation (3) we get:
g - 56 + g + g - 31
Combine like terms:
3g - 87 = 150
[URL='https://www.mathcelebrity.com/1unk.php?num=3g-87%3D150&pl=Solve']Typing this equation into the search engine[/URL], we get:
[B]g = 79[/B]
Plug this into equation (2):
m = 79 - 31
[B]m = 48[/B]
Plug this into equation (4):
d = 79 - 56
[B]d = 23[/B]
Greatest Common Factor and Least Common MultipleFree Greatest Common Factor and Least Common Multiple Calculator - Given 2 or 3 numbers, the calculator determines the following:
* Greatest Common Factor (GCF) using Factor Pairs
* Rewrite Sum using the Distributive Property and factoring out the GCF
* Least Common Multiple (LCM) / Least Common Denominator (LCD) using Factor Pairs
* GCF using the method of Successive Division
* GCF using the Prime Factorization method
* Determine if the numbers are coprime and twin prime
Group CombinationsFree Group Combinations Calculator - Given an original group of certain types of member, this determines how many groups/teams can be formed using a certain condition.
Gym Class Team GeneratorFree Gym Class Team Generator Calculator - Given a list of players, this will randomly generate two teams.
Half of a pepperoni pizza plus 3/4ths of a ham and pineapple pizza has 765 calories. 1/4th of a peppHalf of a pepperoni pizza plus 3/4ths of a ham and pineapple pizza has 765 calories. 1/4th of a pepperoni pizza and a whole ham and pineapple pizza contains 745 calories. How many calories are each of the 2 kinds of pizzas individually?
Let p be the pepperoni pizza calories and h be the ham and pineapple pizza calories. We're given
[LIST=1]
[*]0.5p + 0.75h = 765
[*]0.25p + h = 745
[/LIST]
With this system of equations, we can solve using 3 methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.5p+%2B+0.75h+%3D+765&term2=0.25p+%2B+h+%3D+745&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.5p+%2B+0.75h+%3D+765&term2=0.25p+%2B+h+%3D+745&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.5p+%2B+0.75h+%3D+765&term2=0.25p+%2B+h+%3D+745&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we choose, we get:
[B]h = 580
p = 660[/B]
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Heat IndexFree Heat Index Calculator - Given a temperature in Fahrenheit and a relative humidity percentage, this calculates the Heat Index.
HELP SOLVEA sample mean, sample size, and population standard deviation are given. Use the one-mean z-test to perform the required hypothesis test at the given significance level.
x = 20.5, n = 11, ? = 7, H0: µ = 18.7 , Ha: µ ? 18.7 , ? = 0.01
HELP SOLVEsample mean, sample size, and population standard deviation are given. Use the one-mean z-test to perform the required hypothesis test at the given significance level.
x = 3.7, n = 32, ? = 1.8, H0: µ = 4.2 , Ha: µ ? 4.2 , ? = 0.05
HELP SOLVEA sample mean, sample size, and population standard deviation are given. Use the one-mean z-test to perform the required hypothesis test about the mean, µ, of the population from which the sample was drawn
x = 3.26 , S = 0.55, ?N= 9, H0: µ = 2.85, Ha: µ > 2.85 , ? = 0.01
Henrietta hired a tutor to help her improve her math scores. While working with the tutor, she tookHenrietta hired a tutor to help her improve her math scores. While working with the tutor, she took four tests. She scored 10 points better on the second test than she did on the first, 20 points better on the third test than on the first, and 30 points better on the fourth test than on the first. If the mean of these four tests was 70, what was her score on the third test?
Givens:
[LIST]
[*]Let the first test score be s:
[*]The second test score is: s + 10
[*]The third test score is: s + 20
[*]The fourth test score is: s + 30
[/LIST]
The mean of the four tests is 70, found below:
Sum of test scores / Number of Tests = Mean
Plugging in our number, we get:
(s + s + 10 + s + 20 + s + 30) / 4 = 70
Cross multiply and simplify:
4s + 60 = 70 * 4
4s + 60 = 280
To [URL='https://www.mathcelebrity.com/1unk.php?num=4s%2B60%3D280&pl=Solve']solve this equation for s, we type it in our search engine[/URL] and we get:
s = 55
So the third test score:
s + 20 = 55 + 20
[B]75[/B]
Herfindahl IndexFree Herfindahl Index Calculator - Given a market share of a set of companies, this determines the Herfindahl Index and Normalized Herfindahl Index.
HexagonFree Hexagon Calculator - This calculator solves for side length (s), Area (A), and Perimeter (P) of a hexagon given one of the 3 entries.
Hope it's okay to ask this here?A candy vendor analyzes his sales records and ?nds that if he sells x candy bars in one day, his pro?t(in dollars) is given byP(x) = ? 0.001x2 + 3x ? 1800
(a.) Explain the signi?cance of the number 1800 to the vendor.
(b.) What is the maximum pro?t he can make in one day, and how many candy bars must he sell to
achieve it?
I got 1800 as the amount he starts with, and can't go over. maximum pro?t as 4950
and if I got that right I am getting stuck on how to find how many candy bars.
Thanks
How old am I if 400 reduced by 2 times my age is 244?How old am I if 400 reduced by 2 times my age is 244?
Let my age be a. We're given:
400 - 2a = 244
To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=400-2a%3D244&pl=Solve']type this equation into our search engine [/URL]and we get:
a = [B]78[/B]
How old am I if 400 reduced by 3 times my age is 124?How old am I if 400 reduced by 3 times my age is 124?
Let my age be a. We're given an algebraic expression:
[LIST]
[*]3 times my age means we multiply a by 3: 3a
[*]400 reduced by 3 times my age means we subtract 3a from 400:
[*]400 - 3a
[*]The word [I]is[/I] mean an equation, so we set 400 - 3a equal to 124
[/LIST]
400 - 3a = 124
To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=400-3a%3D124&pl=Solve']we type this equation into our search engine[/URL] and we get:
a = [B]92[/B]
How old am I if: 210 reduced by 3 times my current age is 4 times my current age?How old am I if: 210 reduced by 3 times my current age is 4 times my current age?
Let your current age be a. We're given:
[LIST]
[*]210 reduced by 3 times current age = 210 - 3a
[*]4 times current age = 4a
[*]The word [I]is[/I] means equal to. So we set 210 - 3a equal to 4a
[/LIST]
210 - 3a = 4a
To solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=210-3a%3D4a&pl=Solve']type this equation into our search engine [/URL]and we get:
a = [B]30[/B]
HyperbolaFree Hyperbola Calculator - Given a hyperbola equation, this calculates:
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I am thinking of a number. I multiply it by 14 and add 13. I get the same answer if I multiply by 5I am thinking of a number. I multiply it by 14 and add 13. I get the same answer if I multiply by 5 and add 283. What is my number?
Let the number be n. We're given two expressions:
[LIST=1]
[*]Multiply it by 14 and add 13: 14n + 13
[*]Multiply by 5 and add 283: 5n + 283
[/LIST]
The phrase [I]I get the same answer[/I] means an equation. So we set expression 1 equal to expression 2:
14n + 13 = 5n + 283
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=14n%2B13%3D5n%2B283&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]30[/B]
I am Thinking of a number. I multiply it by 3 and add 67. I get the same answer If i multiply by 6 sI am Thinking of a number. I multiply it by 3 and add 67. I get the same answer If i multiply by 6 subtract 8.
Let the number be n. We're given two equal expressions:
[LIST=1]
[*]3n + 67
[*]6n - 8
[/LIST]
Set the expressions equal to each other since they give the [B]same answer[/B]:
3n + 67 = 6n - 8
We have an equation. [URL='https://www.mathcelebrity.com/1unk.php?num=3n%2B67%3D6n-8&pl=Solve']Type this equation into our search engine and we get[/URL]:
n = [B]25[/B]
I am thinking of a number. I multiply it by 7 and add 25. I get the same answer if I multiply by 3 aI am thinking of a number. I multiply it by 7 and add 25. I get the same answer if I multiply by 3 and add 93. What is my number?
Let the number be n. We're given two expressions:
[LIST]
[*]Multiply the number by 7: 7n
[*]add 25: 7n + 25. <-- Expression 1
[*]Multiply by 3: 3n
[*]Add 93: 3n + 93 <-- Expression 2
[*]The phrase [I]get the same answer[/I] means both expression 1 and expression 2 are equal. So we set them equal to each other:
[/LIST]
7n + 25 = 3n + 93
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=7n%2B25%3D3n%2B93&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]17[/B]
I have saved 24 to buy a game which is three-fourth of the total cost of the game how much does theI have saved 24 to buy a game which is three-fourth of the total cost of the game how much does the game cost ?
Let the cost of the game be c. We're given:
3c/4 = 24
To solve this equation for c, we [URL='https://www.mathcelebrity.com/prop.php?num1=3c&num2=24&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
c = [B]32[/B]
If $349,000 is given to 10 people how much does each person get?If $349,000 is given to 10 people how much does each person get?
Each person gets $349,000 / 10 = [B]$34,900[/B]
If 115% of a number is 460, what is 75% of the numberIf 115% of a number is 460, what is 75% of the number.
Let the number be n. We're given:
115% * n = 460
We write 115% of n as 1.15n, so we have:
1.15n = 460
[URL='https://www.mathcelebrity.com/1unk.php?num=1.15n%3D460&pl=Solve']Using our equation calculator[/URL], we get:
n = [B]400
[/B]
The problem asks for 75% of this number, so we [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=75&den1=400&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']type in [I]75% of 400[/I] into our search engine[/URL] and get:
[B]300[/B]
If 2 & 1/2 pounds of walnuts cost $2.50, how much do walnuts cost per pound?If 2 & 1/2 pounds of walnuts cost $2.50, how much do walnuts cost per pound?
Calculate unit cost given that 2 & 1/2 = 2.5:
2.50 per pound / 2.5 pounds = [B]$1 per pound[/B]
If 3r = 18, what is the value of 6r + 3?2 ways to do this:
[B][U]Method 1[/U][/B]
If 3r = 18, what is the value of 6r + 3?
A) 6
B) 27
C) 36
D) 39
If [URL='https://www.mathcelebrity.com/1unk.php?num=3r%3D18&pl=Solve']we type in the equation 3r = 18 into our search engine[/URL], we get:
r = 6
Take r = 6, and subtitute it into 6r + 3:
6(6) + 3
36 + 3
[B]39 or Answer D
[U]Method 2:[/U][/B]
6r + 3 = 3r(2) = 3
We're given 3r = 18, so we have:
18(2) + 3
36 + 3
[B]39 or Answer D
[MEDIA=youtube]ty3Nk2al1sE[/MEDIA][/B]
If 3x - y = 12, what is the value of 8^x/2^yIf 3x - y = 12, what is the value of 8^x/2^y
We know 8 = 2^3
So using a rule of exponents, we have:
(2^3)^x/2^y
2^(3x)/2^y
Using another rule of exponents, we rewrite this fraction as:
2^(3x -y)
We're given 3x - y = 12, so we have:
[B]2^12[/B]
If 800 feet of fencing is available, find the maximum area that can be enclosed.If 800 feet of fencing is available, find the maximum area that can be enclosed.
Perimeter of a rectangle is:
2l + 2w = P
However, we're given one side (length) is bordered by the river and the fence length is 800, so we have:
So we have l + 2w = 800
Rearranging in terms of l, we have:
l = 800 - 2w
The Area of a rectangle is:
A = lw
Plug in the value for l in the perimeter into this:
A = (800 - 2w)w
A = 800w - 2w^2
Take the [URL='https://www.mathcelebrity.com/dfii.php?term1=800w+-+2w%5E2&fpt=0&ptarget1=0&ptarget2=0&itarget=0%2C1&starget=0%2C1&nsimp=8&pl=1st+Derivative']first derivative[/URL]:
A' = 800 - 4w
Now set this equal to 0 for maximum points:
4w = 800
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%3D800&pl=Solve']Typing this equation into the search engine[/URL], we get:
w = 200
Now plug this into our perimeter equation:
l = 800 - 2(200)
l = 800 - 400
l = 400
The maximum area to be enclosed is;
A = lw
A = 400(200)
A = [B]80,000 square feet[/B]
if a number is added to its square, the result is 72. find the numberif a number is added to its square, the result is 72. find the number.
Let the number be n. We're given:
n + n^2 = 72
Subtract 72 from each side, we get:
n^2 + n - 72 = 0
This is a quadratic equation. [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2%2Bn-72%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']We type this equation into our search engine[/URL], and we get:
[B]n = 8 and n = -9[/B]
If a universal set contains 250 elements, n(A) = 90, n(B) = 125, and n(A ? B) = 35, find n(A ? B)'.If a universal set contains 250 elements, n(A) = 90, n(B) = 125, and n(A ? B) = 35, find n(A ? B)'.
We know from set theory that:
n(A U B) = n(A) + n(B) - n(A ? B)
Plugging in our given values, we get:
n(A U B) = 90 + 125 - 35
n(A U B) = 180
The problem asks for n(A U B)'. This formula is found with:
n(A U B)' = n(U) - n(A U B)
n(U) is the universal set which is 250, so we have:
n(A U B)' = 250 - 180
n(A U B)' = [B]70[/B]
If FG = 9, GH = 4x, and FH = 7x, what is GH?If FG = 9, GH = 4x, and FH = 7x, what is GH?
By segment addition, we have:
FG + GH = FH
Substituting in the values given, we have:
9 + 4x = 7x
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=9%2B4x%3D7x&pl=Solve']type it in our math engine[/URL] and we get:
x = 3
The question asks for GH, so with x = 3, we have:
GH = 4(3)
GH = [B]12[/B]
If Frank’s age is double of Willis’ age and the sum of their ages is 42. What are their ages?If Frank’s age is double of Willis’ age and the sum of their ages is 42. What are their ages?
Let Frank's age be f. Let Willis's age be w. We're given two equations:
[LIST=1]
[*]f = 2w <-- Double means multiply by 2
[*]f + w = 42
[/LIST]
Substitute equation (1) into equation (2):
2w + w = 42
To solve for w, [URL='https://www.mathcelebrity.com/1unk.php?num=2w%2Bw%3D42&pl=Solve']type this equation into our search engine[/URL]. We get:
w = [B]14
[/B]
Now, take w = 14, and substitute it back into equation (1) to solve for f:
f = 2(14)
f = [B]28[/B]
If I add 8 to the number and then multiply the result by 6 I get the same answer as when I add 58 toIf I add 8 to the number and then multiply the result by 6 I get the same answer as when I add 58 to a number. Form an equation
Let the number be n. We're given:
6(n + 8) = n + 58
Multiply through:
6n + 48 = n + 58
To solve this equation for n, [URL='https://www.mathcelebrity.com/1unk.php?num=6n%2B48%3Dn%2B58&pl=Solve']we type it into our search engine[/URL] and we get:
n = [B]2[/B]
If I make 40,000 dollars every 15 minutes then how long will it take me to make a millionIf I make 40,000 dollars every 15 minutes then how long will it take me to make a million
Let f be the number of fifteen minute blocks. We're given:
40000f = 1000000
To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=40000f%3D1000000&pl=Solve']type this equation into our search engine[/URL] and we get:
f = 25
Total minutes = Fifteen minute blocks (f) * 15 minutes
Total minutes = 25 * 15
Total minutes = [B]375 minutes or 6 hours and 15 minutes[/B]
If JK = PQ and PQ = ST, then JK=STIf JK = PQ and PQ = ST, then JK=ST
JK = PQ | Given
Substitute ST for PQ since PQ = ST | Substitution
[B]JK = ST[/B]
If Mr hernandez has 5 times as many students as Mr daniels and together they have 150 students how mIf Mr hernandez has 5 times as many students as Mr daniels and together they have 150 students how many students do each have?
Let h = Mr. Hernandez's students and d = Mr. Daniels students.
We are given two equations:
(1) h = 5d
(2) d + h = 150
Substitute equation (1) into equation (2)
d + (5d) = 150
Combine like terms:
6d = 150
Divide each side of the equation by 6 to isolate d
d = 25 <-- Mr. Daniels Students
Now, plug the value for d into equation (1)
h = 5(25)
h = 125 <-- Mr. Hernandez students
if n(A) = 6, n(A intersect B) = 2 and n(A union B) = 11, find n(B)if n(A) = 6, n(A intersect B) = 2 and n(A union B) = 11, find n(B).
n(A union B) = n(A) + n(B) - n(A intersect B)
Plugging in our given values, we have:
11 = 6 + n(B) - 2
11 = 4 + n(B)
Subtract 4 from each side:
[B]n(B) = 7[/B]
If n(A)=1200, n(B)=1250 and n(AintersectionB)=320, then n(AUB) isIf n(A)=1200, n(B)=1250 and n(AintersectionB)=320, then n(AUB) is
We know that:
n(AUB) = n(A) + n(B) - n(AintersectionB)
Plugging in our given numbers, we get:
n(AUB) = 1200 + 1250 - 320
n(AUB) = [B]2130[/B]
If p = log2(x), what is the value of log2(2x^3) in terms of p?If p = log2(x), what is the value of log2(2x^3) in terms of p?
A. 6p
B. 2p^3
C. 1 + 3p
D. 3 + 3p
E. 1 + p^3
log2(2x^3) = log2(2) + log2(x^3)
log2(2) = 1, so we have:
log2(2x^3) = 1 + 3log2(x)
Since we're given log2(x) = p, we have:
log2(2x^3) = [B]1 + 3p - Answer C
[MEDIA=youtube]-fEkVno3bxs[/MEDIA][/B]
If Quinn has 4 times as many quarters as nickels and they have a combined value of 525 cents, how maIf Quinn has 4 times as many quarters as nickels and they have a combined value of 525 cents, how many of each coin does he have?
Using q for quarters and n for nickels, and using 525 cents as $5.25, we're given two equations:
[LIST=1]
[*]q = 4n
[*]0.25q + 0.05n = 5.25
[/LIST]
Substitute equation (1) into equation (2) for q:
0.25(4n) + 0.05n = 5.25
Multiply through and simplify:
n + 0.05n = 5.25
To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B0.05n%3D5.25&pl=Solve']type it in our search engine[/URL] and we get:
n = [B]5
[/B]
To get q, we plug in n = 5 into equation (1) above:
q = 4(5)
q = [B]20[/B]
if sc = hr and hr=ab then sc=abif sc = hr and hr=ab then sc=ab
sc = hr (given)
Since hr = ab, we can substitute ab for hr by substitution:
[B]sc = ab[/B]
If the circumference of a circular rug is 16? feet, then what is the area of the rug in terms of piIf the circumference of a circular rug is 16? feet, then what is the area of the rug in terms of pi
C = 2pir, so we have:
C = 16?
16? = 2?r
Divide each side by 2?:
r = 16?/2?
r = 8
Now, the area of a circle A is denoted below:
A = ?r^2
Given r = 8 from above, we have:
A = ?(8)^2
A = [B]64?[/B]
If the cost of a bat and a baseball combined is $1.10 and the bat cost $1.00 more than the ball howLet a be the cost of the ball and b be the cost of the bat:
We're given 2 equations:
[LIST=1]
[*]a + b = 1.10
[*]b = a + 1
[/LIST]
Substitute equation (2) into equation (1) for b:
a + a + 1 = 1.10
Combine like terms:
2a + 1 = 1.10
Subtract 1 from each side:
2a + 1 - 1 = 1.10 - 1
2a = 0.10
Divide each side by 2:
2a/2 = 0.10/2
a = [B]0.05[/B]
[MEDIA=youtube]79q346Hy7R8[/MEDIA]
If the diameter of a circle is n, what is the circumference?If the diameter of a circle is n, what is the circumference?
Diameter of a circle = pi(d)
Given d = n, we have:
Diameter = pi(n)
If the perimeter of a rectangular field is 120 feet and the length of one side is 25 feet, how wideIf the perimeter of a rectangular field is 120 feet and the length of one side is 25 feet, how wide must the field be?
The perimeter of a rectangle P, is denoted as:
P = 2l + 2w
We're given l = 25, and P = 120, so we have
2(25) + 2w = 120
Simplify:
2w + 50 = 120
[URL='https://www.mathcelebrity.com/1unk.php?num=2w%2B50%3D120&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 35[/B]
If the perimeter of a rectangular sign is 44cm and the width is 2cm shorter than half the length, thIf the perimeter of a rectangular sign is 44cm and the width is 2cm shorter than half the length, then what are the length and width?
The perimeter (P) of a rectangle is:
2l + 2w = P
We're given P = 44, so we substitute this into the rectangle perimeter equation:
2l + 2w = 44
We're also given w = 0.5l - 2. Substitute the into the Perimeter equation:
2l + 2(0.5l - 2) = 44
Multiply through and simplify:
2l + l - 4 = 44
Combine like terms:
3l - 4 = 44
[URL='https://www.mathcelebrity.com/1unk.php?num=3l-4%3D44&pl=Solve']Type this equation into the search engine[/URL], and we get:
[B]l = 16[/B]
Substitute this back into the equation w = 0.5l - 2
w = 0.5(16) - 2
w = 8 - 2
[B]w = 6[/B]
If the probability of an event occurring is 7%, what is the probability of an event not occurring?If the probability of an event occurring is 7%, what is the probability of an event not occurring?
The probability of all event is 1, or 100%.
If we treat the success of an event as p, then q is 1 - p.
Using percentages, we have:
q = 100% - p
Given p = 7%, we have:
q = 100% - 7%
q = [B]93%[/B]
if the ratio of 2x to 5y is 3 to 4, what is the ratio of x to y?if the ratio of 2x to 5y is 3 to 4, what is the ratio of x to y?
Set up our given ratio:
2x/5y = 3/4
Cross multiply:
2x * 4 = 5y * 3
8x = 15y
Divide each side by 8:
8x/8 = 15y/8
x = 15y/8
Now divide each side by y to find x/y:
x/y = 15y/8y
x/y =[B] 15/8[/B]
if two angles are supplementary and congruent then they are right anglesif two angles are supplementary and congruent then they are right angles
Let the first angle be x. Let the second angle be y.
Supplementary angles means their sum is 180:
x + y = 180
We're given both angles are congruent, meaning equal. So we set x = y:
y + y = 180
To solve for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=y%2By%3D180&pl=Solve']type this equation into our search engine[/URL] and we get:
y = [B]90. <-- 90 degrees is a right angle, so this is TRUE[/B]
If x = 2y/3 and y = 18, what is the value of 2x - 3?If x = 2y/3 and y = 18, what is the value of 2x - 3?
A) 21
B) 15
C) 12
D) 10
Substitute the values into the equation:
2(2y/3) - 3 <-- Given x = 2y/3
Simplifying, we have:
4y/3 - 3
Now substitute y = 18 into this:
4(18)/3 - 3
4(6) - 3
24 - 3
[B]21 or Answer A[/B]
If you divide my brother's age by 3 and then add 20, you will get my age, which is 31. What is my brIf you divide my brother's age by 3 and then add 20, you will get my age, which is 31. What is my brothers age?
Let b be the brother's age.
We're given the following relationship for the brother's age and my age:
b/3 + 20 = 31
Subtract 20 from each side:
b/3 + 20 - 20 = 31 - 20
Cancel the 20's on the left side and we get:
b/3 = 11
Cross multiply, and we get:
b = 3 * 11
b = [B]33
[/B]
Check our work using b = 33 for b/3 + 20 = 31:
33/3 + 20 ? 31
11 + 20 ? 31
31 = 31
If your parents give you $20 per week and $1.50 per chore, how many chores would you have to do to eIf your parents give you $20 per week and $1.50 per chore, how many chores would you have to do to earn a total of $33.50 that week?
Let c be the number of chores. We're given the equation:
1.50c + 20 = 33.50
To solve this equation for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=1.50c%2B20%3D33.50&pl=Solve']type it in our search engine [/URL]and we get:
c = [B]9[/B]
In 16 years, Ben will be 3 times as old as he is right nowIn 16 years, Ben will be 3 times as old as he is right now.
Let Ben's age today be a. We're given:
a + 16 = 3a
[URL='https://www.mathcelebrity.com/1unk.php?num=a%2B16%3D3a&pl=Solve']Type this equation into the search engine[/URL], and we get:
a = [B]8[/B]
In 20 years charles will be 3 times as old as he is now. How old is he now?In 20 years charles will be 3 times as old as he is now. How old is he now?
Let Charles's age be a today. We're given:
a + 20 = 3a
[URL='https://www.mathcelebrity.com/1unk.php?num=a%2B20%3D3a&pl=Solve']If we type this equation into our search engine[/URL], we get:
[B]a = 10
[/B]
Let's check our work in our given equation:
10 + 20 ? 3(10)
30 = 30 <-- Checks out!
In 56 years, Stella will be 5 times as old as she is right now.In 56 years, Stella will be 5 times as old as she is right now.
Let Stella's age be s. We're given:
s + 56 = 5s
[URL='https://www.mathcelebrity.com/1unk.php?num=s%2B56%3D5s&pl=Solve']Type this equation into our search engine[/URL], and we get:
[B]s = 14[/B]
In a class there are 5 more boys than girls. There are 13 students in all. How many boys are there iIn a class there are 5 more boys than girls. There are 13 students in all. How many boys are there in the class?
We start by declaring variables for boys and girls:
[LIST]
[*]Let b be the number of boys
[*]Let g be the number of girls
[/LIST]
We're given two equations:
[LIST=1]
[*]b = g + 5
[*]b + g = 13
[/LIST]
Substitute equation (1) for b into equation (2):
g + 5 + g = 13
Grouping like terms, we get:
2g + 5 = 13
Subtract 5 from each side:
2g + 5 - 5 = 13 - 5
Cancel the 5's on the left side and we get:
2g = 8
Divide each side of the equation by 2 to isolate g:
2g/2 = 8/2
Cancel the 2's on the left side and we get:
g = 4
Substitute g = 4 into equation (1) to solve for b:
b = 4 + 5
b = [B]9[/B]
In a factory that manufactures tires, a machine responsible for molding the tire has a failure rateIn a factory that manufactures tires, a machine responsible for molding the tire has a failure rate of 0.2%. If 1,000 tires are produced in a day, of which 6 are faulty, what is the difference between the experimental probability and the theoretical probability?
Theoretical probability = Failure Rate * Tires
Theoretical probability = 0.002 * 1000
Theoretical probability = 2
The experimental probability was given as 6, so the difference is:
6 - 2 = [B]4[/B]
In a given year, Houston has good air quality 48% of the days, moderate air quality 41% of the days,In a given year, Houston has good air quality 48% of the days, moderate air quality 41% of the days, and unhealthy air quality 4% of the days. How many days per year do residents have unhealthy air quality?
4% of 365 days in a year = [B]14.6 days. If we are talking full days, we have 14.[/B]
In a golf tournament Ned was 4 under par on Saturday and 5 over or on Sunday. What is the differenceIn a golf tournament Ned was 4 under par on Saturday and 5 over or on Sunday. What is the difference in his score on Sunday compared to his score on Saturday
Givens and opening thoughts:
[LIST]
[*]Think of par as 0 or average.
[*]Under par is negative
[*]Over par is positive
[*]We have 4 under par as -4
[*]We have 5 over par as +5
[/LIST]
The difference is found by subtracting:
+5 - -4
+5 + 4
[B]9 strokes[/B]
In a hurricane the wind pressure varies directly as the square of the wind velocity. If a wind presIn a hurricane the wind pressure varies directly as the square of the wind velocity. If a wind pressure is a measure of a hurricane's destruction capacity, what happens to this destructive power when the wind speed doubles?
Let P = pressure and v = velocity (wind speed)
We are given p = v^2
Double velocity, so we have a new pressure P2:
P2 = (2v)^2
P2 = 4v^2
Compare the 2:
p = v^2
p = 4v^2
Doubling the wind speed [B]quadruples, or 4 times[/B] the pressure.
In a newspaper, it was reported that yearly robberies in Springfield were up 50% to 351 in 2013 fromIn a newspaper, it was reported that yearly robberies in Springfield were up 50% to 351 in 2013 from 2012. How many robberies were there in Springfield in 2012?
Let the robberies in 2012 be r. We're given the following equation:
1.5r = 351 <-- We write a 50% increase as 1.5
To solve this equation for r, we [URL='https://www.mathcelebrity.com/1unk.php?num=1.5r%3D351&pl=Solve']type it into our search engine[/URL] and we get:
r = [B]234[/B]
In an algebra test, the highest grade was 50 points higher than the lowest grade. The sum of the twoIn an algebra test, the highest grade was 50 points higher than the lowest grade. The sum of the two grades was 180.
Let the high grade be h and the low grade be l. We're given:
[LIST=1]
[*]h = l + 50
[*]h + l = 180
[/LIST]
Substitute equation (1) into equation (2) for h
l + 50 + l = 180
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=l%2B50%2Bl%3D180&pl=Solve']we type it in our search engine[/URL] and we get:
l = [B]65
[/B]
Now, we take l = 65 and substitute it into equation (1) to solve for h:
h = 65 + 50
h = [B]115[/B]
In x years time, Peter will be 23 years old. How old is he now?In x years time, Peter will be 23 years old. How old is he now?
Let Peter's current age be a. In x years time means we add x to a, so we're given:
a + x = 23
We want to find a, s we subtract x from each side to get:
a + x - x = 23 - x
Cancel the x terms on the left side and we get:
a = [B]23 - x[/B]
Inclusive Number Word ProblemsFree Inclusive Number Word Problems Calculator - Given an integer A and an integer B, this calculates the following inclusive word problem questions:
1) The Average of all numbers inclusive from A to B
2) The Count of all numbers inclusive from A to B
3) The Sum of all numbers inclusive from A to B
Incremental Cash FlowFree Incremental Cash Flow Calculator - Given cash inflows, outflows, depreciable amounts, and tax rates, this determines the incremental cash flows.
Input TableFree Input Table Calculator - Given an input table with input and output values, this will determine the operator and rule used to populate the missing values.
Installment Sales Method of AccountingFree Installment Sales Method of Accounting Calculator - Given a sales price, cost amount, installment payment amount and term, this will show the accounting for the Installment Payment method.
InterpolationFree Interpolation Calculator - Given a set of data, this interpolates using the following methods:
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* Nearest Neighbor (Piecewise Constant)
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Interval PartitionFree Interval Partition Calculator - Given a partitioned interval, this evaluates the norm (mesh) by calculating each subinterval
Isosceles TriangleFree Isosceles Triangle Calculator - Given a long side (a) and a short side (b), this determines the following items of the isosceles triangle:
* Area (A)
* Semi-Perimeter (s)
* Altitude a (ha)
* Altitude b (hb)
* Altitude c (hc)
It costs $4.25 per game at the bowling alley plus $1.90 to rent shoes. if Wayne has $20, how many gaIt costs $4.25 per game at the bowling alley plus $1.90 to rent shoes. if Wayne has $20, how many games can he Bowl?
Let g be the number of games. The cost for Wayne is:
C(g) = Cost per game * number of games + shoe rental
4.25g + 1.90 = C(g)
We're given C(g) = 20, so we have:
4.25g + 1.90 = 20
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=4.25g%2B1.90%3D20&pl=Solve']equation solver[/URL] for g, we get:
g = 4.25
We need whole games, we we round down to [B]4 games[/B]
Jack has 34 bills and coins in 5’s and 2’s. The total value is $116. How many 5 dollar bills does heJack has 34 bills and coins in 5’s and 2’s. The total value is $116. How many 5 dollar bills does he have?
Let the number of 5 dollar bills be f. Let the number of 2 dollar bills be t. We're given two equations:
[LIST=1]
[*]f + t = 34
[*]5f + 2t = 116
[/LIST]
We have a system of equations, which we can solve 3 ways:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+34&term2=5f+%2B+2t+%3D+116&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+34&term2=5f+%2B+2t+%3D+116&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+34&term2=5f+%2B+2t+%3D+116&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answers:
[LIST]
[*][B]f = 16[/B]
[*][B]t = 18[/B]
[/LIST]
Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolaJack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolates to each of his friends and still had 2 chocolates left.
If Jack had 2 chocolates left, then the total given to his friends is:
50 - 2 = 48
Let f be the number of friends at his birthday party. Then we have:
3f = 48
[URL='https://www.mathcelebrity.com/1unk.php?num=3f%3D48&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]f = 16[/B]
Jake Callahan stars in the new TV series Stone Simons: Kid Astronaut. The day after the first episodJake Callahan stars in the new TV series Stone Simons: Kid Astronaut. The day after the first episode airs, Jake receives a bunch of fan mail. He splits all the letters into 3 equal stacks to open with his mom and his sister. Each stack contains 21 letters. Which equation can you use to find the number of letters n Jake receives?
The number of letters n is represented by number of stacks (s) times letter per stack (l). We're given s = 3 and l = 21, so we have:
n = 21(3)
n = [B]63[/B]
James is four time as old as peter if their combined age is 30 how old is James.James is four time as old as peter if their combined age is 30 how old is James.
Let j be Jame's age. Let p be Peter's age. We're given:
[LIST=1]
[*]j = 4p
[*]j + p = 30
[/LIST]
Substitute (1) into (2)
4p + p = 30
Combine like terms:
5p = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=5p%3D30&pl=Solve']Type 5p = 30 into our search engine[/URL], and we get p = 6.
Plug p = 6 into equation (1) to get James's age, we get:
j = 4(6)
j = [B]24[/B]
Janet drove 395 kilometers and the trip took 5 hours. How fast was Janet traveling?Janet drove 395 kilometers and the trip took 5 hours. How fast was Janet traveling?
Distance = Rate * Time
We're given D = 395 and t = 5
We want Rate. We divide each side of the equation by time:
Distance / Time = Rate * Time / Time
Cancel the Time's on each side and we get:
Rate = Distance / Time
Plugging our numbers in, we get:
Rate = 395/5
Rate = [B]79 kilometers[/B]
Jason has an equal number of nickels and dimes. The total value of his nickels and dimes is $2.25. HJason has an equal number of nickels and dimes. The total value of his nickels and dimes is $2.25. How many nickels does Jason have?
Let the number of nickels be n
Let the number of dimes be d
We're given two equations:
[LIST=1]
[*]d = n
[*]0.05n + 0.1d = 2.25
[/LIST]
Substitute equation (1) for d into equation (2):
0.05n + 0.1n = 2.25
Solve for [I]n[/I] in the equation 0.05n + 0.1n = 2.25
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(0.05 + 0.1)n = 0.15n
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
0.15n = + 2.25
[SIZE=5][B]Step 3: Divide each side of the equation by 0.15[/B][/SIZE]
0.15n/0.15 = 2.25/0.15
n = [B]15[/B]
[URL='https://www.mathcelebrity.com/1unk.php?num=0.05n%2B0.1n%3D2.25&pl=Solve']Source[/URL]
Jennifer added $120 to her savings account during July. If this brought her balance to $700, how mucJennifer added $120 to her savings account during July. If this brought her balance to $700, how much has she saved previously?
We have a starting balance s. We're given:
s + 120 = 700
To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B120%3D700&pl=Solve']type it in our search engine[/URL] and we get:
s = [B]580[/B]
Jennifer has 26 less than triple the savings of Matthew. Matthew has saved 81. How much has JenniferJennifer has 26 less than triple the savings of Matthew. Matthew has saved 81. How much has Jennifer saved?
Let Jennifer's savings be j. We're given:
j = 3(81) - 26
j = 243 - 26
j = [B]217[/B]
Jennifer is twice as old as Peter. The difference between their ages is 15. What is Peters ageJennifer is twice as old as Peter. The difference between their ages is 15. What is Peters age
Let j be Jennifer's age
Let p be Peter's age
We're given two equations:
[LIST=1]
[*]j = 2p
[*]j - p = 15
[/LIST]
Substitute equation (1) into equation (2) for j
2p - p = 15
To solve for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=2p-p%3D15&pl=Solve']type this equation into our calculation engine[/URL] and we get:
p = [B]15[/B]
Jenny threw the javelin 4 metres further than Angus but 5 metres less than Cameron. if the combinedJenny threw the javelin 4 metres further than Angus but 5 metres less than Cameron. if the combined distance thrown by the 3 friends is 124 metres, how far did Angus throw the javelin?
Assumptions and givens:
[LIST]
[*]Let a be the distance Angus threw the javelin
[*]Let c be the distance Cameron threw the javelin
[*]Let j be the distance Jenny threw the javelin
[/LIST]
We're given 3 equations:
[LIST=1]
[*]j = a + 4
[*]j = c - 5
[*]a + c + j = 124
[/LIST]
Since j is the common variable in all 3 equations, let's rearrange equation (1) and equation (2) in terms of j as the dependent variable:
[LIST=1]
[*]a = j - 4
[*]c = j + 5
[*]a + c + j = 124
[/LIST]
Now substitute equation (1) and equation (2) into equation (3) for a and c:
j - 4 + j + 5 + j = 124
To solve this equation for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=j-4%2Bj%2B5%2Bj%3D124&pl=Solve']type it in our math engine[/URL] and we get:
j = 41
The question asks how far Angus (a) threw the javelin. Since we have Jenny's distance j = 41 and equation (1) has j and a together, let's substitute j = 41 into equation (1):
a = 41 - 4
a = [B]37 meters[/B]
Jill and Jack are getting vegetables from the Farmer's Market. Jill buys 12 carrots and 8 tomatoes fJill and Jack are getting vegetables from the Farmer's Market. Jill buys 12 carrots and 8 tomatoes for $34. Jack buys 10 carrots and 7 tomatoes for $29. How much does each carrot and each tomato cost?
Let the cost of carrots be c and the cost of tomatoes be t. Since the total cost is price times quantity, We're given two equations:
[LIST=1]
[*]12c + 8t = 34 <-- Jill
[*]10c + 7t = 29 <-- Jack
[/LIST]
We have a system of equations. We can solve this one of three ways:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12c+%2B+8t+%3D+34&term2=10c+%2B+7t+%3D+29&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12c+%2B+8t+%3D+34&term2=10c+%2B+7t+%3D+29&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12c+%2B+8t+%3D+34&term2=10c+%2B+7t+%3D+29&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we choose, we get:
[LIST]
[*][B]t = 2[/B]
[*][B]c = 1.5[/B]
[/LIST]
Jim is 9 years older than June. Alex is 8 years younger than June. If the total of their ages is 82,Jim is 9 years older than June. Alex is 8 years younger than June. If the total of their ages is 82, how old is the eldest of them
Let j be Jim's age, a be Alex's age, and u be June's age. We have 3 given equations:
[LIST=1]
[*]j + a + u = 82
[*]j = u + 9
[*]a = u - 8
[/LIST]
Substitute (2) and (3) into (1)
(u + 9) + (u - 8) + u = 82
Combine Like Terms:
3u + 1 = 82
[URL='https://www.mathcelebrity.com/1unk.php?num=3u%2B1%3D82&pl=Solve']Type this equation into the search engine[/URL], and we get u = 27.
The eldest (oldest) of the 3 is Jim. So we have from equation (2)
j = u + 9
j = 27 + 9
[B]j = 36[/B]
Jim works for his dad and earns $400 every week plus $22 for every chair (c) he sells. Write an equaJim works for his dad and earns $400 every week plus $22 for every chair (c) he sells. Write an equation that can be used to determine jims weekly salary (S) given the number of chairs (c) he sells.
[B]S(c) = 400 + 22c[/B]
Jimmy was given $16 for washing the dog.He now has $47. How much money did he start with?Jimmy was given $16 for washing the dog. He now has $47. How much money did he start with?
Let his starting money be s. We're told:
s + 16 = 47
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B16%3D47&pl=Solve']type this equation into our search engin[/URL]e and we get:
s = [B]31[/B]
Jinas final exam has true/false questions, worth 3 points each, and multiple choice questions, worthJinas final exam has true/false questions, worth 3 points each, and multiple choice questions, worth 4 points each. Let x be the number of true/false questions she gets correct, and let y be the number of multiple choice questions she gets correct. She needs at least 76 points on the exam to get an A in the class. Using the values and variables given, write an inequality describing this.
At least means greater than or equal to, so we have:
[B]3x + 4y >= 76[/B]
Joe worked in a shoe department where he earned $325 weekly and 6.5% commission on all of his sales.Joe worked in a shoe department where he earned $325 weekly and 6.5% commission on all of his sales. What was joe’s total sales if he earned $507 last week
Let s be total Sales. 6.5% is 0.065 as a decimal, so Joe's earnings are given by:
0.065s + 325 = 507
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.065s%2B325%3D507&pl=Solve']type this equation into our math engine[/URL] and we get:
s = [B]2800[/B]
Joel bought 88 books. Some books cost $13 each and some cost $17 each. In all, he spent $128. WhichJoel bought 88 books. Some books cost $13 each and some cost $17 each. In all, he spent $128. Which system of linear equations represents the given situation?
Let a be the number of the $13 book, and b equal the number of $17 books. We have the following system of linear equations:
[LIST=1]
[*][B]a + b = 88[/B]
[*][B]13a + 17b = 128[/B]
[/LIST]
To solve this system, use our calculator for the following methods:
[LIST]
[*][URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+b+%3D+88&term2=13a+%2B+17b+%3D+128&pl=Substitution']Substitution[/URL]
[*][URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+b+%3D+88&term2=13a+%2B+17b+%3D+128&pl=Elimination']Elimination[/URL]
[*][URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+b+%3D+88&term2=13a+%2B+17b+%3D+128&pl=Cramers+Method']Cramers Method[/URL]
[/LIST]
Joey and Romnick play in the same soccer team. Last Saturday, Romnick scored 3 more goals than Joey,Joey and Romnick play in the same soccer team. Last Saturday, Romnick scored 3 more goals than Joey,but together they scored less than 9 goals. What are the possible number of goal Romnick scored?
Let j be Joey's goals
Let r by Romnick's goals
We're given 1 equation and 1 inequality:
[LIST=1]
[*]r = j + 3
[*]r + j < 9
[/LIST]
Rearranging equation 1 for j, we have:
[LIST=1]
[*]j = r - 3
[*]r + j < 9
[/LIST]
Substitute equation (1) into inequality (2) for j:
r + r - 3 < 9
2r - 3 < 9
[URL='https://www.mathcelebrity.com/1unk.php?num=2r-3%3C9&pl=Solve']Typing this inequality into our math engine[/URL], we get:
[B]r < 6[/B]
Joint Variation EquationsFree Joint Variation Equations Calculator - Given a joint variation (jointly proportional) of a variable between two other variables with a predefined set of conditions, this will create the joint variation equation and solve based on conditions.
Also called combined variation.
Jow buys 9 CD’s for the same price, and also a cassette tape for $9.45. His total bill was 118.89. WJow buys 9 CD’s for the same price, and also a cassette tape for $9.45. His total bill was 118.89. What was the cost of one CD?
Let the price of each cd be c. We're given the equation:
9c + 9.45 = 118.89
[URL='https://www.mathcelebrity.com/1unk.php?num=9c%2B9.45%3D118.89&pl=Solve']We type this equation into our search engine[/URL] and we get:
c = [B]12.16[/B]
JP's age is twice the age of Reyna. The sum of their ages does not exceed 51JP's age is twice the age of Reyna. The sum of their ages does not exceed 51
Let JP's age be j. Let Reyna's age be r. We're given two expressions:
[LIST=1]
[*]w = 2r
[*]r + w <= 51. ([I]Does not exceed means less than or equal to)[/I]
[/LIST]
We substitute (1) into (2) for w to get the inequality:
r + 2r <= 51
To solve this inequality, we type it in our search engine and we get:
[B]r <= 17[/B]
Juan is going on a flight to the beach. his luggage weighs 36 pounds. The bag weighs 4 pounds more tJuan is going on a flight to the beach. his luggage weighs 36 pounds. The bag weighs 4 pounds more than the weight of 2 small bags of beach toys. Which equation can be used to find the weight in pounds of each bag of beach toys?
Let b be the weight of each bag of beach toys. We're given the following relationship:
2b -4 = 36
To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=2b-4%3D36&pl=Solve']type it in our math engine[/URL] and we get:
b = [B]20[/B]
Julia owes 18.20 for the month of November. Her plan costs 9.00 for the first 600 text messages andJulia owes 18.20 for the month of November. Her plan costs 9.00 for the first 600 text messages and .10 cents for additional texts. How many texts did she send out?
Let m be the number of messages. We have a cost function of:
C(m) = 9 + 0.1(m - 600)
We are given C(m) = 18.20
18.20 = 9 + 0.1(m - 600)
18.20 = 9 + 0.1m - 60
Combine like terms:
18.20 = 0.1m - 51
Add 51 to each side
0.1m = 69.20
Divide each side by 0.1
[B]m = 692[/B]
Justin is older than Martina. The difference in their ages is 22 and the sum of their ages is 54. WhJustin is older than Martina. The difference in their ages is 22 and the sum of their ages is 54. What age is Martina?
[U]Assumptions and givens:[/U]
[LIST]
[*]Let Justin's age be j
[*]Let Martina's age be m
[*]j > m ([I]since Justin is older than Martina[/I])
[/LIST]
We're given the following equations :
[LIST=1]
[*]j - m = 22
[*]j + m = 54
[/LIST]
Since the coefficients of m are opposites, we can take a shortcut using the [I]elimination method[/I] and add equation (1) to equation (2)
(j + j) + (m - m) = 22 + 54
2j = 76
To solve for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=2j%3D76&pl=Solve']type this equation into our math engine[/URL] and we get:
j = 38
The question asks for Martina's age (m), so we can pick equation (1) or equation (2). Let's use equation (1):
38 - m = 22
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=38-m%3D22&pl=Solve']type it in our math engine[/URL] and we get:
m = [B]16[/B]
Kamara has a square fence kennel area for her dogs in the backyard. The area of the kennel is 64 ftKamara has a square fence kennel area for her dogs in the backyard. The area of the kennel is 64 ft squared. What are the dimensions of the kennel? How many feet of fencing did she use? Explain.
Area of a square with side length (s) is:
A = s^2
Given A = 64, we have:
s^2 = 64
[URL='https://www.mathcelebrity.com/radex.php?num=sqrt(64%2F1)&pl=Simplify+Radical+Expression']Typing this equation into our math engine[/URL], we get:
s = 8
Which means the dimensions of the kennel are [B]8 x 8[/B].
How much fencing she used means perimeter. The perimeter P of a square with side length s is:
P = 4s
[URL='https://www.mathcelebrity.com/square.php?num=8&pl=Side&type=side&show_All=1']Given s = 8, we have[/URL]:
P = 4 * 8
P = [B]32[/B]
kate is twice as old as her sister mars. the sum of their ages is 24. find their ages.kate is twice as old as her sister mars. the sum of their ages is 24. find their ages.
Let k be Kate's age
Let m be Mars's age
We're given two equations:
[LIST=1]
[*]k = 2m. (Because twice means multiply by 2)
[*]k + m = 24
[/LIST]
Substitute equation (1) for k into equation (2):
2m + m = 24
T o solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=2m%2Bm%3D24&pl=Solve']type this equation into our math engine[/URL]:
m = [B]8
[/B]
We want to solve for k using m= 8. Substitute this into equation 1
k = 2(8)
k = [B]16
[/B]
Check our work for equation 1
16 = 2 * 8
16 = 16
Check our work for equation 2
16 + 8 ? 24
24 = 24
[MEDIA=youtube]TJMTRYP-Ct8[/MEDIA]
Kate spent 1 more than Lauren, and together they spent 5Kate spent 1 more than Lauren, and together they spent 5.
Let k be the amount Kate spent, and l be the amount Lauren spent. We're given:
[LIST=1]
[*]k = l + 1
[*]k + l = 5
[/LIST]
Substitute (1) into (2):
(l + 1) + l = 5
Group like terms
2l + 1 = 5
[URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B1%3D5&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]l = 2[/B]
Plug this into Equation (1), we get:
k = 2 + 1
[B]k = 3
[/B]
Kate Spent 3, and Lauren spent 2
Kate spent at most $2.50 on apples and oranges. She bought 5 apples at $0.36 each. What is the mostKate spent at most $2.50 on apples and oranges. She bought 5 apples at $0.36 each. What is the most She spent on oranges
[U]Assumptions and givens:[/U]
[LIST]
[*]Let a be the total cost of apples
[*]Let o be the total cost of oranges
[/LIST]
The phrase [I]at most[/I] means less than or equal to, so we have:
a + o <= 2.50
[U]Find the cost of apples (a)[/U]
a = price per apple * quantity of apples
a = 0.36 * 5
a = 1.8
Our new inequality with a = 1.8 is:
1.8 + o <= 2.50
[URL='https://www.mathcelebrity.com/1unk.php?num=1.8%2Bo%3C%3D2.50&pl=Solve']Typing this inequality into our search engine[/URL], we get:
[B]o <= 0.7[/B]
Kelly took clothes to the cleaners 3 times last month. First, she brought 4 shirts and 1 pair of slaKelly took clothes to the cleaners 3 times last month. First, she brought 4 shirts and 1 pair of slacks and paid11.45. Then she brought 5 shirts, 3 pairs of slacks, and 1 sports coat and paid 27.41. Finally, she brought 5 shirts and 1 sports coat and paid 16.94. How much was she charged for each shirt, each pair of slacks, and each sports coat?
Let s be the cost of shirts, p be the cost of slacks, and c be the cost of sports coats. We're given:
[LIST=1]
[*]4s + p = 11.45
[*]5s + 3p + c = 27.41
[*]5s + c = 16.94
[/LIST]
Rearrange (1) by subtracting 4s from each side:
p = 11.45 - 4s
Rearrange (3)by subtracting 5s from each side:
c = 16.94 - 5s
Take those rearranged equations, and plug them into (2):
5s + 3(11.45 - 4s) + (16.94 - 5s) = 27.41
Multiply through:
5s + 34.35 - 12s + 16.94 - 5s = 27.41
[URL='https://www.mathcelebrity.com/1unk.php?num=5s%2B34.35-12s%2B16.94-5s%3D27.41&pl=Solve']Group like terms using our equation calculator [/URL]and we get:
[B]s = 1.99 [/B] <-- Shirt Cost
Plug s = 1.99 into modified equation (1):
p = 11.45 - 4(1.99)
p = 11.45 - 7.96
[B]p = 3.49[/B] <-- Slacks Cost
Plug s = 1.99 into modified equation (3):
c = 16.94 - 5(1.99)
c = 16.94 - 9.95
[B]c = 6.99[/B] <-- Sports Coat cost
Kendra is half as old as Morgan and 3 years younger than Lizzie. The total of their ages is 39. HowKendra is half as old as Morgan and 3 years younger than Lizzie. The total of their ages is 39. How old are they?
Let k be Kendra's age, m be Morgan's age, and l be Lizzie's age. We're given:
[LIST=1]
[*]k = 0.5m
[*]k = l - 3
[*]k + l + m = 39
[/LIST]
Rearranging (1) by multiplying each side by 2, we have:
m = 2k
Rearranging (2) by adding 3 to each side, we have:
l = k + 3
Substituting these new values into (3), we have:
k + (k + 3) + (2k) = 39
Group like terms:
(k + k + 2k) + 3 = 39
4k + 3 = 39
[URL='https://www.mathcelebrity.com/1unk.php?num=4k%2B3%3D39&pl=Solve']Type this equation into the search engine[/URL], and we get:
[B]k = 9
[/B]
Substitute this back into (1), we have:
m = 2(9)
[B]m = 18
[/B]
Substitute this back into (2), we have:
l = (9) + 3
[B][B]l = 12[/B][/B]
Kevin and randy have a jar containing 41 coins, all of which are either quarters or nickels. The totKevin and randy have a jar containing 41 coins, all of which are either quarters or nickels. The total value of the jar is $7.85. How many of each type?
Let d be dimes and q be quarters. Set up two equations from our givens:
[LIST=1]
[*]d + q = 41
[*]0.1d + 0.25q = 7.85
[/LIST]
[U]Rearrange (1) by subtracting q from each side:[/U]
(3) d = 41 - q
[U]Now, substitute (3) into (2)[/U]
0.1(41 - q) + 0.25q = 7.85
4.1 - 0.1q + 0.25q = 7.85
[U]Combine q terms[/U]
0.15q + 4.1 = 7.85
[U]Using our [URL='http://www.mathcelebrity.com/1unk.php?num=0.15q%2B4.1%3D7.85&pl=Solve']equation calculator[/URL], we get:[/U]
[B]q = 25[/B]
[U]Substitute q = 25 into (3)[/U]
d = 41 - 25
[B]d = 16[/B]
Kevin ran 4 miles more than Steve ran. The sum of their distances is 26 miles. How far did Steve runKevin ran 4 miles more than Steve ran. The sum of their distances is 26 miles. How far did Steve run? The domain of the solution is:
Let k be Kevin's miles ran
Let s be Steve's miles ran
We have 2 given equtaions:
[LIST=1]
[*]k = s + 4
[*]k + s = 26
[/LIST]
Substitute (1) into (2)
(s + 4) + s = 26
2s + 4 = 26
Plug this into our [URL='http://www.mathcelebrity.com/1unk.php?num=2s%2B4%3D26&pl=Solve']equation calculator[/URL] and we get s = 11
Kiko is now 6 times as old as his sister. In 6 years, he will be 3 times as old as his sister. WhatKiko is now 6 times as old as his sister. In 6 years, he will be 3 times as old as his sister. What is their present age?
Let k be Kiko's present age
Let s be Kiko's sisters age.
We're given two equations:
[LIST=1]
[*]k = 6s
[*]k + 6 = 3(s + 6)
[/LIST]
To solve this system of equations, we substitute equation (1) into equation (2) for k:
6s + 6 = 3(s + 6)
[URL='https://www.mathcelebrity.com/1unk.php?num=6s%2B6%3D3%28s%2B6%29&pl=Solve']Typing this equation into our math engine[/URL] to solve for s, we get:
s = [B]4[/B]
To solve for k, we substitute s = 4 into equation (1) above:
k = 6 * 4
k = [B]24[/B]
Kimberly wants to become a member of the desert squad at a big catering company very badly, but sheKimberly wants to become a member of the desert squad at a big catering company very badly, but she must pass three difficult tests to do so. On the first Terrifying Tiramisu test she scored a 68. On the second the challenging Chocalate-Sprinkled Creme Brulee she scored a 72. If kimberly needs an average of 60 on all three tests to become a member on the squad what is the lowest score she can make on her third and final test
This is a missing average problem.
Given 2 scores of 68, 72, what should be score number 3 in order to attain an average score of 60?
[SIZE=5][B]Setup Average Equation:[/B][/SIZE]
Average = (Sum of our 2 numbers + unknown score of [I]x)/[/I]Total Numbers
60 = (68 + 72 + x)/3
[SIZE=5][B]Cross Multiply[/B][/SIZE]
68 + 72 + x = 60 x 3
x + 140 = 180
[SIZE=5][B]Subtract 140 from both sides of the equation to isolate x:[/B][/SIZE]
x + 140 - 140 = 180 - 140
x = [B]40[/B]
Kinematic EquationsFree Kinematic Equations Calculator - Given the 5 inputs of the 4 kinematic equations, this will solve any of the equations it can based on your inputs for the kinematics.
KitesFree Kites Calculator - This calculates perimeter and/or area of a kite given certain inputs such as short and long side, short and long diagonal, or angle between short and long side
Kris wants to fence in her square garden that is 40 feet on each side. If she places posts every 10Kris wants to fence in her square garden that is 40 feet on each side. If she places posts every 10 feet, how many posts will she need?
Perimeter (P) of a square with side s:
P = 4s
Given s = 40, we have:
P = 4(40)
P = 160 feet
160 feet / 10 foot spaces = [B]16 posts[/B]
larger of 2 numbers is 12 more than the smaller number. if the sum of the 2 numbers is 74 find the 2larger of 2 numbers is 12 more than the smaller number. if the sum of the 2 numbers is 74 find the 2 numbers
Declare Variables for each number:
[LIST]
[*]Let l be the larger number
[*]Let s be the smaller number
[/LIST]
We're given two equations:
[LIST=1]
[*]l = s + 12
[*]l + s = 74
[/LIST]
Equation (1) already has l solved for. Substitute equation (1) into equation (2) for l:
s + 12 + s = 74
Solve for [I]s[/I] in the equation s + 12 + s = 74
[SIZE=5][B]Step 1: Group the s terms on the left hand side:[/B][/SIZE]
(1 + 1)s = 2s
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
2s + 12 = + 74
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 12 and 74. To do that, we subtract 12 from both sides
2s + 12 - 12 = 74 - 12
[SIZE=5][B]Step 4: Cancel 12 on the left side:[/B][/SIZE]
2s = 62
[SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE]
2s/2 = 62/2
s = [B]31[/B]
To solve for l, we substitute in s = 31 into equation (1):
l = 31 + 12
l = [B]43[/B]
larger of 2 numbers is 4 more than the smaller. the sum of the 2 is 40. what is the larger number?larger of 2 numbers is 4 more than the smaller. the sum of the 2 is 40. what is the larger number?
Declare variables for the 2 numbers:
[LIST]
[*]Let l be the larger number
[*]Let s be the smaller number
[/LIST]
We're given two equations:
[LIST=1]
[*]l = s + 4
[*]l + s = 40
[/LIST]
To get this problem in terms of the larger number l, we rearrange equation (1) in terms of l.
Subtract 4 from each side in equation (1)
l - 4 = s + 4 - 4
Cancel the 4's and we get:
s = l - 4
Our given equations are now:
[LIST=1]
[*]s = l - 4
[*]l + s = 40
[/LIST]
Substitute equation (1) into equation (2) for s:
l + l - 4 = 40
Grouping like terms for l, we get:
2l - 4 = 40
Add 4 to each side:
2l - 4 + 4 = 40 + 4
Cancelling the 4's on the left side, we get
2l = 44
Divide each side of the equation by 2 to isolate l:
2l/2 = 44/2
Cancel the 2's on the left side and we get:
l = [B]22[/B]
Length (l) is the same as width (w) and their product is 64.Length (l) is the same as width (w) and their product is 64.
We're given 2 equations:
[LIST=1]
[*]lw = 64
[*]l = w
[/LIST]
Substitute equation (2) into equation (1):
w * w = 64
w^2 = 64
[B]w = 8[/B]
Since l = w, then [B]l = 8[/B]
Letter Arrangements in a WordFree Letter Arrangements in a Word Calculator - Given a word, this determines the number of unique arrangements of letters in the word.
Line Equation-Slope-Distance-Midpoint-Y interceptFree Line Equation-Slope-Distance-Midpoint-Y intercept Calculator - Enter 2 points, and this calculates the following:
* Slope of the line (rise over run) and the line equation y = mx + b that joins the 2 points
* Midpoint of the two points
* Distance between the 2 points
* 2 remaining angles of the rignt triangle formed by the 2 points
* y intercept of the line equation
* Point-Slope Form
* Parametric Equations and Symmetric Equations
Or, if you are given a point on a line and the slope of the line including that point, this calculates the equation of that line and the y intercept of that line equation, and point-slope form.
Also allows for the entry of m and b to form the line equation
Linear CongruenceFree Linear Congruence Calculator - Given an modular equation ax ≡ b (mod m), this solves for x if a solution exists
Linear ConversionsFree Linear Conversions Calculator - Converts to and from the following linear measurements for a given quantity:
Inches
Feet
Yards
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Littles LawFree Littles Law Calculator - Given two out of the three inputs for Littles Law, Throughput (TH), Cycle Time (CT, and WIP, this solves for the third item.
Logan is 8 years older than 4 times the age of his nephew. Logan is 32 years old. How old is his nepLogan is 8 years older than 4 times the age of his nephew. Logan is 32 years old. How old is his nephew?
Let the age of Logan's nephew be n. We're given:
4n + 8 = 32 (Since [I]older[/I] means we add)
To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=4n%2B8%3D32&pl=Solve']type it into our search engine[/URL] and we get:
[B]n = 6[/B]
Logistic MapFree Logistic Map Calculator - Given r, x0 and (n) trials, this will display the logistic map.
Lois is purchasing an annuity that will pay $5,000 annually for 20 years, with the first annuity payLois is purchasing an annuity that will pay $5,000 annually for 20 years, with the first annuity payment made on the date of purchase. What is the value of the annuity on the purchase date given a discount rate of 7 percent?
This is an annuity due, since the first payment is made on the date of purchase.
Using our [URL='http://www.mathcelebrity.com/annimmpv.php?pv=&av=&pmt=5000&n=20&i=7&check1=2&pl=Calculate']present value of an annuity due calculator[/URL], we get [B]56,677.98[/B].
Lorda is older than Kate. The sum of their ages is 30. The difference in their ages is 6. What are tLorda is older than Kate. The sum of their ages is 30. The difference in their ages is 6. What are their ages?
Let Lorda's age be l. Let Kate's age be k. We're given two equations:
[LIST=1]
[*]l + k = 30
[*]l - k = 6 <-- Since Lorda is older
[/LIST]
Add the 2 equations together and we eliminate k:
2l = 36
[URL='https://www.mathcelebrity.com/1unk.php?num=2l%3D36&pl=Solve']Typing this equation into our search engine[/URL] and solving for l, we get:
l = [B]18[/B]
Now substitute l = 18 into equation 1:
18 + k = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=18%2Bk%3D30&pl=Solve']Type this equation into our search engine[/URL] and solving for k, we get:
k = [B]12[/B]
Lotto Drawing ProbabilityFree Lotto Drawing Probability Calculator - Given a lotto drawing with a Pick(x) out of (y) total choices, this calculates the probability of winning that lottery picking all (x) correct numbers.
Luke and Dan's total debt is $72. If Luke's debt is three times Dan's debt, what is Dan's debt?Luke and Dan's total debt is $72. If Luke's debt is three times Dan's debt, what is Dan's debt?
Let Dan's debt be d.
Let Luke's debt be l.
We're given two equations:
[LIST=1]
[*]d + l = 72
[*]l = 3d
[/LIST]
Substitute equation (2) for l into equation (1):
d + 3d = 72
Solve for [I]d[/I] in the equation d + 3d = 72
[SIZE=5][B]Step 1: Group the d terms on the left hand side:[/B][/SIZE]
(1 + 3)d = 4d
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
4d = + 72
[SIZE=5][B]Step 3: Divide each side of the equation by 4[/B][/SIZE]
4d/4 = 72/4
d = [B]18[/B]
M is the midpoint of AB. Prove AB = 2AMM is the midpoint of AB. Prove AB = 2AM
M is the midpoint of AB (Given)
AM = MB (Definition of Congruent Segments)
AM + MB = AB (Segment Addition Postulate)
AM + AM = AB (Substitution Property of Equality)
2AM = AB (Distributive property)
[MEDIA=youtube]8BNo_4kvBzw[/MEDIA]
Maggie earns $10 each hour she works at the pet store and $0.25 for each phone call she answers. MagMaggie earns $10 each hour she works at the pet store and $0.25 for each phone call she answers. Maggie answered 60 phone calls and earned $115 last week
Set up an equation where c is the number of phone calls Maggie answers and h is the number of hours Maggie worked:
0.25c + 10h = 115
We're given c = 60, so we have:
0.25(60) + 10h = 115
15 + 10h = 115
We want to solve for h. So we[URL='https://www.mathcelebrity.com/1unk.php?num=15%2B10h%3D115&pl=Solve'] type this equation into our search engine[/URL] and we get:
h = [B]10[/B]
MAPE - MPE - MAPDFree MAPE - MPE - MAPD Calculator - Given a time series of actual and forecasted values, this determines the following:
* Mean Absolute Percentage Error (MAPE) also known as the Mean Absolute Percentage Deviation (MAPD)
* Symmetric Mean Absolute Percentage Error (sMAPE)
* Mean Absolute Percentage Error (MPE)
Marcela is having a presidential debate watching party with all of her friends, She will be making cMarcela is having a presidential debate watching party with all of her friends, She will be making chicken wings and hot dogs. Each chicken wing costs $2 to make and each hot dog costs $3. She needs to spend at least $500. Marcela knows that she will make more than 50 chicken wings and hot dogs combined. She also knows that she will make less than 120 chicken wings and less that 100 hot dogs. What are her inequalities?
Let c be the number of chicken wings and h be the number of hot dogs. Set up the given inequalities:
[LIST=1]
[*]c + h > 50 [I]Marcela knows that she will make more than 50 chicken wings and hot dogs combined.[/I]
[*]2c + 3h >= 500 [I]She needs to spend at least $500[/I]
[*]c < 120 [I]She also knows that she will make less than 120 chicken wings[/I]
[*]h < 100 [I]and less that 100 hot dogs[/I]
[/LIST]
Margin of Error from Confidence IntervalFree Margin of Error from Confidence Interval Calculator - Given a confidence interval, this determines the margin of error and sample mean.
Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are nowMaria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now only 22 boxes left. With how many did she start?
Let the number of boxes Maria started with be b. We're given the following pieces:
[LIST]
[*]She starts with b
[*]She bought 7 boxes. So we add 7 to b: b + 7
[*]If half the boxes were destroyed, she's left with 1/2. So we divide (b + 7)/2
[*]Only 22 boxes left means we set (b + 7)/2 equal to 22
[/LIST]
(b + 7)/2 = 22
Cross multiply:
b + 7 = 22 * 2
b + 7 = 44
[URL='https://www.mathcelebrity.com/1unk.php?num=b%2B7%3D44&pl=Solve']Type this equation into our search engine[/URL] to solve for b and we get:
b = [B]37[/B]
Mark and Jennie are bowling. Jennie’s score is double Mark’s score. If the sum of their score is 171Mark and Jennie are bowling. Jennie’s score is double Mark’s score. If the sum of their score is 171, find each person’s score by writing out an equation.
Let Mark's score be m. Let Jennie's score be j. We're given two equations:
[LIST=1]
[*]j = 2m
[*]j + m = 171
[/LIST]
Substitute equation (1) into equation (2):
2m + m = 171
[URL='https://www.mathcelebrity.com/1unk.php?num=2m%2Bm%3D171&pl=Solve']Type this equation into our search engine[/URL] to solve for m:
m = [B]57
[/B]
To solve for j, we substitute m = 57 in equation (1) above:
j = 2(57)
j = [B]114[/B]
Markov ChainFree Markov Chain Calculator - Given a transition matrix and initial state vector, this runs a Markov Chain process.
Markup MarkdownFree Markup Markdown Calculator - Given the 3 items of a markup word problem, cost, markup percentage, and sale price, this solves for any one of the three given two of the items. This works as a markup calculator, markdown calculator.
Martha is 18 years older than Harry. Their ages add to 106. Write an equation and solve it to find tMartha is 18 years older than Harry. Their ages add to 106. Write an equation and solve it to find the ages of Martha and Harry.
Let m be Martha's age. Let h be Harry's age. We're given two equations:
[LIST=1]
[*]m = h + 18 [I](older means we add)[/I]
[*]h + m = 106
[/LIST]
Substitute equation (1) into equation (2) for m:
h + h + 18 = 106
To solve for h, [URL='https://www.mathcelebrity.com/1unk.php?num=h%2Bh%2B18%3D106&pl=Solve']we type this equation into our search engine[/URL] and we get:
h = [B]44[/B]
Martha's age 2/3 of her brother's age. Martha is 24 years old now. How old is her brother?Martha's age 2/3 of her brother's age. Martha is 24 years old now. How old is her brother?
Let her brother's age be b. We're given:
2b/3 = 24
To solve this proportion for b, [URL='https://www.mathcelebrity.com/prop.php?num1=2b&num2=24&den1=3&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']we type it in our search engine[/URL] and we get:
b = [B]36[/B]
Matrix PropertiesFree Matrix Properties Calculator - Given a matrix |A|, this calculates the following items if they exist:
* Determinant = det(A)
* Inverse = A-1
* Transpose = AT
* Adjoint = adj(A)
* Eigen equation (characteristic polynomial) = det|λI - A|
* Trace = tr(A)
* Gauss-Jordan Elimination using Row Echelon and Reduced Row Echelon Form
* Dimensions of |A| m x n
* Order of a matrix
* Euclidean Norm ||A||
* Magic Sum if it exists
* Determines if |A| is an Exchange Matrix
Max and Bob went to the store. Max bought 2 burgers and 2 drinks for $5.00 bob bought 3 burgers andMax and Bob went to the store. Max bought 2 burgers and 2 drinks for $5.00. Bob bought 3 burgers and 1 drink for $5.50. How much is each burger and drink?
[U]Set up the givens where b is the cost of a burger and d is the cost of a drink:[/U]
Max: 2b + 2d = 5
Bob: 3b + d = 5.50
[U]Rearrange Bob's equation by subtracting 3b from each side[/U]
(3) d = 5.50 - 3b
[U]Now substitute that d equation back into Max's Equation[/U]
2b + 2(5.50 - 3b) = 5
2b + 11 - 6b = 5
[U]Combine b terms:[/U]
-4b + 11 = 5
[U]Subtract 11 from each side[/U]
-4b = -6
[U]Divide each side by -4[/U]
b = 3/2
[B]b = $1.50[/B]
[U]Now plug that back into equation (3):[/U]
d = 5.50 - 3(1.50)
d = 5.50 - 4.50
[B]d = $1.00[/B]
Max is 23 years younger than his father.Together their ages add up to 81.Max is 23 years younger than his father.Together their ages add up to 81.
Let Max's age be m, and his fathers' age be f. We're given:
[LIST=1]
[*]m = f - 23 <-- younger means less
[*]m + f = 81
[/LIST]
Substitute Equation (1) into (2):
(f - 23) + f = 81
Combine like terms to form the equation below:
2f - 23 = 81
[URL='https://www.mathcelebrity.com/1unk.php?num=2f-23%3D81&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]f = 52[/B]
Substitute this into Equation (1):
m = 52 - 23
[B]m = 29[/B]
Max's age is 2 more than his fathers age divided by 4. Max is 13 years old. How old is his dad?Max's age is 2 more than his fathers age divided by 4. Max is 13 years old. How old is his dad?
Let Max's father be age f. We're given:
(f + 2)/4 = 13
Cross Multiply:
f + 2 = 52
[URL='https://www.mathcelebrity.com/1unk.php?num=f%2B2%3D52&pl=Solve']Typing this equation into the search engine[/URL], we get:
f = [B]50[/B]
Mcnemar TestFree Mcnemar Test Calculator - Given a 2 x 2 contingency table and a significance level, this will determine the test statistic, critical value, and hypothesis conclusion using a Mcnemar test.
Melissa runs a landscaping business. She has equipment and fuel expenses of $264 per month. If she cMelissa runs a landscaping business. She has equipment and fuel expenses of $264 per month. If she charges $53 for each lawn, how many lawns must she service to make a profit of at $800 a month?
Melissa has a fixed cost of $264 per month in fuel. No variable cost is given. Our cost function is:
C(x) = Fixed Cost + Variable Cost. With variable cost of 0, we have:
C(x) = 264
The revenue per lawn is 53. So R(x) = 53x where x is the number of lawns.
Now, profit is Revenue - Cost. Our profit function is:
P(x) = 53x - 264
To make a profit of $800 per month, we set P(x) = 800.
53x - 264 = 800
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=53x-264%3D800&pl=Solve']equation solver[/URL], we get:
[B]x ~ 21 lawns[/B]
Method of Equated Time-Exact Method-Macaulay Duration-VolatilityFree Method of Equated Time-Exact Method-Macaulay Duration-Volatility Calculator - Given a set of cash flows at certain times, and a discount rate, this will calculate t using the equated time method and the exact method, as well as the macaulay duration and volatility
Midpoint formulaMidpoint formula
Given two points (x1, y1) and (x2, y2), the midpoint is found as the average distance between the 2 points:
[LIST]
[*]x value is: (x1 + x2)/2
[*]y value is: (y1 + y2)/2
[/LIST]
So our midpoint is:
((x1 + x2)/2, (y1 + y2)/2)
Mindy and troy combined ate 9 pieces of the wedding cake. Mindy ate 3 pieces of cake and troy had 1Mindy and troy combined ate 9 pieces of the wedding cake. Mindy ate 3 pieces of cake and troy had 1/4 of the total cake. Write an equation to determine how many pieces of cake (c) that were in total
Let c be the total number of pieces of cake. Let m be the number of pieces Mindy ate. Let t be the number of pieces Troy ate. We have the following given equations:
[LIST]
[*]m + t = 9
[*]m = 3
[*]t = 1/4c
[/LIST]
Combining (2) and (3) into (1), we have:
3 + 1/4c = 9
Subtract 3 from each side:
1/4c = 6
Cross multiply:
[B]c = 24
[MEDIA=youtube]aeqWQXr5f_Y[/MEDIA][/B]
Missing AverageFree Missing Average Calculator - Given a set of scores and an average, this calculates the next score necessary to attain that average
Modified Internal Rate of Return (MIRR)Free Modified Internal Rate of Return (MIRR) Calculator - Given a set of positive/negative cash flows, a finance rate, and a reinvestment rate, this calculates the modified internal rate of return
Modified Payback PeriodFree Modified Payback Period Calculator - Given a set of cash inflows, outflows, and a discount rate, this calculates the modified payback period.
ModulusFree Modulus Calculator - Given 2 integers a and b, this modulo calculator determines a mod b or simplifies modular arithmetic such as 7 mod 3 + 5 mod 8 - 32 mod 5
Molly is making strawberry infused water. For each ounce of strawberry juice, she uses two times asMolly is making strawberry infused water. For each ounce of strawberry juice, she uses three times as many ounces of water as juice. How many ounces of strawberry juice and how many ounces of water does she need to make 40 ounces of strawberry infused water?
Let j be the ounces of strawberry juice and w be the ounces of water. We're given:
[LIST=1]
[*]j + w = 40
[*]w = 3j
[/LIST]
Substitute (2) into (1):
j + 3j = 40
Combine like terms:
4j = 40
[URL='https://www.mathcelebrity.com/1unk.php?num=4j%3D40&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]j = 10[/B]
From equation (2), we substitute j = 2:
w = 3(10)
[B]w = 30
[/B]
This means we have [B]10 ounces of juice[/B] and [B]30 ounces of water[/B] for a 40 ounce mix.
Money MultiplierFree Money Multiplier Calculator - Given a reserve ratio and initial deposit amount, this calculates the money multiplier and displays the re-lending process table for a bank to other banks including reserves and loans.
Morse Code TranslatorFree Morse Code Translator Calculator - Given a phrase with letters, numbers, and most punctuation symbols, the calculator will perform the following duties:
1) Translate that phrase to Morse Code.
2) Translate the Morse Code to a Dit-Dah message
3) Calculate the number of dots in the message
4) Calculate the number of dashes in the message
This also translates from Morse Code back to English.
MortgageFree Mortgage Calculator - Calculates the monthly payment, APY%, total value of payments, principal/interest/balance at a given time as well as an amortization table on a standard or interest only home or car loan with fixed interest rate. Handles amortized loans.
Mr turner sent his car to the workshop for repair work as well as to change 4 tires. Mr turner paidMr turner sent his car to the workshop for repair work as well as to change 4 tires. Mr turner paid $1035 in all. The repair work cost 5 times the price of each tire. The mechanic told Mr. turner that the repair work cost $500. Explain the mechanic’s mistake
Let the cost for work be w. Let the cost for each tire be t. We're given;
[LIST=1]
[*]w = 5t
[*]w + 4t = 1035
[/LIST]
Substitute equation 1 into equation 2:
(5t) + 4t = 1035
[URL='https://www.mathcelebrity.com/1unk.php?num=%285t%29%2B4t%3D1035&pl=Solve']Type this equation into our search engine[/URL], and we get:
t = 115
Substitute this into equation (1):
w = 5(115)
w = [B]575[/B]
The mechanic underestimated the work cost.
Mr. Tan has two daughters. His elder daughter is 1/3 of his age while his younger daughter is 1/4 ofMr. Tan has two daughters. His elder daughter is 1/3 of his age while his younger daughter is 1/4 of his age. If Mr. Tan’s age is 60, how old are his elder and youngest daughter?
Let Mr. Tan's age be a. We're given:
[LIST]
[*]Elder Daughter's age = 60/3 = [B]20 years old[/B]
[*]Younger Daughter's age = 60/4 = [B]15 years old[/B]
[/LIST]
Ms. Jeffers is splitting $975 among her three sons. If the oldest gets twice as much as the youngestMs. Jeffers is splitting $975 among her three sons. If the oldest gets twice as much as the youngest and the middle son gets $35 more than the youngest, how much does each boy get?
Let 0 be the oldest son, m be the middle sun, and y be the youngest son. Set up our given equations
[LIST]
[*]o = 2y
[*]m = y + 35
[*]o + m + y = 975
[/LIST]
[U]Substitute the first and second equations into Equation 3[/U]
2y + y + 35 + y = 975
[U]Combine the y terms[/U]
4y + 35 = 975
Subtract 35 using our [URL='http://www.mathcelebrity.com/1unk.php?num=4y%2B35%3D975&pl=Solve']equation calculator[/URL] to solve and get [B]y = 235[/B]
[U]Plug y = 235 into equation 2[/U]
m = 235 + 35
[B]m = 270[/B]
[U]Plug y = 235 into equation 2[/U]
o = 2(235)
[B]o = 470[/B]
Multinomial DistributionFree Multinomial Distribution Calculator - Given a set of xi counts and a respective set of probabilities θi, this calculates the probability of those events occurring.
n and m are congruent and supplementary. prove n and m are right anglesn and m are congruent and supplementary. prove n and m are right angles
Given:
[LIST]
[*]n and m are congruent
[*]n and m are supplementary
[/LIST]
If n and m are supplementary, that means we have the equation:
m + n = 180
We're also given n and m are congruent, meaning they are equal. So we can substitute n = m into the supplementary equation:
m + m = 180
To solve this equation for m, [URL='https://www.mathcelebrity.com/1unk.php?num=m%2Bm%3D180&pl=Solve']we type it in our search engine[/URL] and we get:
m = 90
This means m = 90, n = 90, which means they are both right angles since by definition, a right angle is 90 degrees.
Nancy is 10 years less than 3 times her daughters age. If Nancy is 41 years old, how old is her daugNancy is 10 years less than 3 times her daughters age. If Nancy is 41 years old, how old is her daughter?
Declare variables for each age:
[LIST]
[*]Let Nancy's age be n
[*]Let her daughter's age be d
[/LIST]
We're given two equations:
[LIST=1]
[*]n = 3d - 10
[*]n = 41
[/LIST]
We set 3d - 10 = 41 and solve for d:
Solve for [I]d[/I] in the equation 3d - 10 = 41
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants -10 and 41. To do that, we add 10 to both sides
3d - 10 + 10 = 41 + 10
[SIZE=5][B]Step 2: Cancel 10 on the left side:[/B][/SIZE]
3d = 51
[SIZE=5][B]Step 3: Divide each side of the equation by 3[/B][/SIZE]
3d/3 = 51/3
d = [B]17[/B]
Net Present Value (NPV) - Internal Rate of Return (IRR) - Profitability IndexFree Net Present Value (NPV) - Internal Rate of Return (IRR) - Profitability Index Calculator - Given a series of cash flows Ct at times t and a discount rate of (i), the calculator will determine the Net Present Value (NPV) at time 0, also known as the discounted cash flow model.
Profitability Index
Also determines an Internal Rate of Return (IRR) based on a series of cash flows. NPV Calculator
Nick is given $50 to spend on a vacation . He decides to spend $5 a day. Write an equation that showNick is given $50 to spend on a vacation . He decides to spend $5 a day. Write an equation that shows how much money Nick has after x amount of days.
Set up the function M(x) where M(x) is the amount of money after x days. Since spending means a decrease, we subtract to get:
[B]M(x) = 50 - 5x[/B]
Nick said that his sister is 4 times as old as his brother, and together their ages add to 20 compleNick said that his sister is 4 times as old as his brother, and together their ages add to 20 complete this equation to find his brothers age
Let b be the brother's age and s be the sister's age. We're given two equations:
[LIST=1]
[*]s =4b
[*]b + s = 20
[/LIST]
Plug (1) into (2):
b + 4b = 20
[URL='https://www.mathcelebrity.com/1unk.php?num=b%2B4b%3D20&pl=Solve']Type this equation into the search engine[/URL], and we get:
[B]b = 4[/B]
Nicole is half as old as Donald. The sum of their ages is 72. How old is Nicole in years?Nicole is half as old as Donald. The sum of their ages is 72. How old is Nicole in years?
Let n be Nicole's age. Let d be Donald's age. We're given two equations:
[LIST=1]
[*]n = 0.5d
[*]n + d = 72
[/LIST]
Substitute equation (1) into (2):
0.5d + d = 72
1.5d = 72
[URL='https://www.mathcelebrity.com/1unk.php?num=1.5d%3D72&pl=Solve']Typing this equation into the search engine and solving for d[/URL], we get:
d = [B]48[/B]
Nine workers are hired to harvest potatoes from a field. Each is given a plot which is 5x5 feet in sNine workers are hired to harvest potatoes from a field. Each is given a plot which is 5x5 feet in size. What is the total area of the field?
Area of each plot is 5x5 = 25 square feet.
Total area = Area per plot * number of plots
Total area = 25 sq ft * 9
Total area = [B]225 sq ft[/B]
Nominal YieldFree Nominal Yield Calculator - Given an effective annual rate of interest based on a compounding period, this determines the nominal yield.
Number Line MidpointFree Number Line Midpoint Calculator - Calculates a midpoint between 2 points on a number line or finds the second endpoint if one endpoint and midpoint are given.
numerator of a fraction is 5 less than its denominator. if 1 is added to the numerator and to the denumerator of a fraction is 5 less than its denominator. if 1 is added to the numerator and to the denominator the new fraction is 2/3. find the fraction.
Let n be the numerator.
Let d be the denominator.
We're given 2 equations:
[LIST=1]
[*]n = d - 5
[*](n + 1)/(d + 1) = 2/3
[/LIST]
Substitute equation (1) into equation (2) for n:
(d - 5 + 1) / (d + 1) = 2/3
(d - 4) / (d + 1) = 2/3
Cross multiply:
3(d - 4) = 2(d + 1)
To solve this equation for d, we type it in our search engine and we get:
d = 14
Substitute d = 14 into equation (1) to solve for n:
n = 14 - 5
n = 9
Therefore, our fraction n/d is:
[B]9/14[/B]
Oceanside Bike Rental Shop charges $15.00 plus $9.00 per hour for renting a bike. Dan paid $51.00 toOceanside Bike Rental Shop charges $15.00 plus $9.00 per hour for renting a bike. Dan paid $51.00 to rent a bike. How many hours was he hiking for?
Set up the cost equation C(h) where h is the number of hours needed to rent the bike:
C(h) = Cost per hour * h + rental charge
Using our given numbers in the problem, we have:
C(h) = 9h + 15
The problem asks for h, when C(h) = 51.
9h + 15 = 51
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=9h%2B15%3D51&pl=Solve']plug this equation into our search engine[/URL] and we get:
h = [B]4[/B]
Odds ProbabilityFree Odds Probability Calculator - Given an odds prediction m:n of an event success, this calculates the probability that the event will occur or not occur
Of all smokers in particular district, 40% prefer brand A and 60% prefer brand B. Of those who prefeOf all smokers in particular district, 40% prefer brand A and 60% prefer brand B. Of those who prefer brand A, 30% are female, and of those who prefer brand B, 40% are female.
Q: What is the probability that a randomly selected smoker prefers brand A, given that the person selected is a female?
P(F) = P(F|A)*P(A) + P(F|B)*P(B)
P(F) = 0.3*0.4 + 0.4*0.6 = 0.36
So, 36% of all the smokers are female.
You are looking for P(A|F)
P(A|F) = P(A and F)/P(F)
P(A|F) = (P(F|A)*P(A))/P(F)
P(A|F) = (0.3 * 0.4)/0.36
P(A|F) = [B]0.33 or 33%[/B]
On an algebra test, the highest grade was 42 points higher than the lowest grade. The sum of the twoOn an algebra test, the highest grade was 42 points higher than the lowest grade. The sum of the two grades was 138. Find the lowest grade.
[U]Let h be the highest grade and l be the lowest grade. Set up the given equations:[/U]
(1) h = l + 42
(2) h + l = 138
[U]Substitute (1) into (2)[/U]
l + 42 + l = 138
[U]Combine l terms[/U]
2l + 42 = 138
[U]Enter that equation into our [URL='http://www.mathcelebrity.com/1unk.php?num=2l%2B42%3D138&pl=Solve']equation calculator[/URL] to get[/U]
[B]l = 48
[/B]
[U]Substitute l = 48 into (1)[/U]
h = 48 + 42
[B]h = 90[/B]
On Monday the office staff at your school paid 8.77 for 4 cups of coffee and 7 bagels. On WednesdayOn Monday the office staff at your school paid 8.77 for 4 cups of coffee and 7 bagels. On Wednesday they paid 15.80 for 8 cups of coffee and 14 bagels. Can you determine the cost of a bagel
Let the number of cups of coffee be c
Let the number of bagels be b.
Since cost = Price * Quantity, we're given two equations:
[LIST=1]
[*]7b + 4c = 8.77
[*]14b + 8c = 15.80
[/LIST]
We have a system of equations. We can solve this 3 ways:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=7b+%2B+4c+%3D+8.77&term2=14b+%2B+8c+%3D+15.80&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=7b+%2B+4c+%3D+8.77&term2=14b+%2B+8c+%3D+15.80&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=7b+%2B+4c+%3D+8.77&term2=14b+%2B+8c+%3D+15.80&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we use, we get the same answer
[LIST]
[*]The system is inconsistent. Therefore, we have no answer.
[/LIST]
On the first day of ticket sales the school sold 3 senior citizen tickets and 10 child tickets for aOn the first day of ticket sales the school sold 3 senior citizen tickets and 10 child tickets for a total of $82. The school took in $67 on the second day by selling 8 senior citizen tickets And 5 child tickets. What is the price of each ticket?
Let the number of child tickets be c
Let the number of senior citizen tickets be s
We're given two equations:
[LIST=1]
[*]10c + 3s = 82
[*]5c + 8s = 67
[/LIST]
We have a system of simultaneous equations. We can solve it using any one of 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we choose, we get:
[LIST]
[*][B]c = 7[/B]
[*][B]s = 4[/B]
[/LIST]
One number exceeds another by 15. The sum of the numbers is 51. What are these numbersOne number exceeds another by 15. The sum of the numbers is 51. What are these numbers?
Let the first number be x, and the second number be y. We're given two equations:
[LIST=1]
[*]x = y + 15
[*]x + y = 51
[/LIST]
Plug (1) into (2)
(y + 15) + y = 51
Combine like terms:
2y + 15 = 51
[URL='https://www.mathcelebrity.com/1unk.php?num=2y%2B15%3D51&pl=Solve']Plug this equation into the search engine[/URL] and we get:
[B]y = 18[/B]
Now plug this into (1) to get:
x = 18 + 15
[B]x = 33[/B]
One number is 1/4 of another number. The sum of the two numbers is 25. Find the two numbers. Use a cOne number is 1/4 of another number. The sum of the two numbers is 25. Find the two numbers. Use a comma to separate your answers.
Let the first number be x and the second number be y. We're given:
[LIST=1]
[*]x = 1/4y
[*]x + y = 25
[/LIST]
Substitute (1) into (2)
1/4y + y = 25
Since 1/4 = 0.25, we have:
0.25y + y = 25
[URL='https://www.mathcelebrity.com/1unk.php?num=0.25y%2By%3D25&pl=Solve']Type this equation into the search engine[/URL] to get:
[B]y = 20
[/B]
Now, substitute this into (1) to solve for x:
x = 1/4y
x = 1/4(20)
[B]x = 5
[/B]
The problem asks us to separate the answers by a comma. So we write this as:
[B](x, y) = (5, 20)[/B]
One number is 1/5 of another number. The sum of the two numbers is 18. Find the two numbers.One number is 1/5 of another number. The sum of the two numbers is 18. Find the two numbers.
Let the two numbers be x and y. We're given:
[LIST=1]
[*]x = 1/5y
[*]x + y = 18
[/LIST]
Substitute (1) into (2):
1/5y + y = 18
1/5 = 0.2, so we have:
1.2y = 18
[URL='https://www.mathcelebrity.com/1unk.php?num=1.2y%3D18&pl=Solve']Type 1.2y = 18 into the search engine[/URL], and we get [B]y = 15[/B].
Which means from equation (1) that:
x = 15/5
[B]x = 3
[/B]
Our final answer is [B](x, y) = (3, 15)[/B]
One number is 3 times another. Their sum is 44.One number is 3 times another. Their sum is 44.
Let the first number be x, and the second number be y. We're given:
[LIST=1]
[*]x = 3y
[*]x + y = 44
[/LIST]
Substitute (1) into (2):
3y + y = 44
[URL='https://www.mathcelebrity.com/1unk.php?num=3y%2By%3D44&pl=Solve']Type this equation into the search engine[/URL], and we get:
[B]y = 11[/B]
Plug this into equation (1):
x = 3(11)
[B]x = 33[/B]
one number is 3 times as large as another. Their sum is 48. Find the numbersone number is 3 times as large as another. Their sum is 48. Find the numbers
Let the first number be x. Let the second number be y. We're given two equations:
[LIST=1]
[*]x = 3y
[*]x + y = 48
[/LIST]
Substitute equation (1) into equation (2):
3y + y = 48
To solve for y, [URL='https://www.mathcelebrity.com/1unk.php?num=3y%2By%3D48&pl=Solve']we type this equation into the search engine[/URL] and we get:
[B]y = 12[/B]
Now, plug y = 12 into equation (1) to solve for x:
x = 3(12)
[B]x = 36[/B]
One number is 8 times another number. The numbers are both positive and have a difference of 70.One number is 8 times another number. The numbers are both positive and have a difference of 70.
Let the first number be x, the second number be y. We're given:
[LIST=1]
[*]x = 8y
[*]x - y = 70
[/LIST]
Substitute(1) into (2)
8y - y = 70
[URL='https://www.mathcelebrity.com/1unk.php?num=8y-y%3D70&pl=Solve']Plugging this equation into our search engine[/URL], we get:
[B]y = 10[/B] <-- This is the smaller number
Plug this into Equation (1), we get:
x = 8(10)
[B]x = 80 [/B] <-- This is the larger number
One number is equal to the square of another. Find the numbers if both are positive and their sum isOne number is equal to the square of another. Find the numbers if both are positive and their sum is 650
Let the number be n. Then the square is n^2. We're given:
n^2 + n = 650
Subtract 650 from each side:
n^2 + n - 650 = 0
We have a quadratic equation. [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2%2Bn-650%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']We type this into our search engine[/URL] and we get:
n = 25 and n = -26
Since the equation asks for a positive solution, we use [B]n = 25[/B] as our first solution.
the second solution is 25^2 = [B]625[/B]
one number is twice a second number. the sum of those numbers is 45one number is twice a second number. the sum of those numbers is 45.
Let the first number be x and the second number be y. We're given:
[LIST=1]
[*]x = 2y
[*]x + y = 45
[/LIST]
Substitute Equation (1) into Equation (2):
2y + y = 45
[URL='https://www.mathcelebrity.com/1unk.php?num=2y%2By%3D45&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]y = 15[/B]
Plug this into equation (1) to solve for x, and we get:
x = 2(15)
[B]x = 30[/B]
One positive number is one-fifth of another number. The difference between the two numbers is 192, fOne positive number is one-fifth of another number. The difference between the two numbers is 192, find the numbers.
Let the first number be x and the second number be y. We're given two equations:
[LIST=1]
[*]x = y/5
[*]x + y = 192
[/LIST]
Substitute equation 1 into equation 2:
y/5 + y = 192
Since 1 equals 5/5, we rewrite our equation like this:
y/5 = 5y/5 = 192
We have fractions with like denominators, so we add the numerators:
(1 + 5)y/5 = 192
6y/5 = 192
[URL='https://www.mathcelebrity.com/prop.php?num1=6y&num2=192&den1=5&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Type this equation into our search engine[/URL], and we get:
[B]y = 160[/B]
Substitute this value into equation 1:
x = 160/5
x = [B]32[/B]
Opposite NumbersFree Opposite Numbers Calculator - Given a positive or negative integer (n), this calculates the opposite number of n
Ordered and Unordered PartitionsFree Ordered and Unordered Partitions Calculator - Given a population size (n) and a group population of (m), this calculator determines how many ordered or unordered groups of (m) can be formed from (n)
Ordering NumbersFree Ordering Numbers Calculator - Given a list of numbers, this will order the list ascending (lowest to highest or least to greatest) or descending (highest to lowest or greatest to least)
P-Hat Confidence IntervalFree P-Hat Confidence Interval Calculator - Given a large sized distribution, and a success amount for a certain criteria x, and a confidence percentage, this will calculate the confidence interval for that criteria.
Pam has two part-time jobs. At one job, she works as a cashier and makes $8 per hour. At the secondPam has two part-time jobs. At one job, she works as a cashier and makes $8 per hour. At the second job, she works as a tutor and makes$12 per hour. One week she worked 30 hours and made$268 . How many hours did she spend at each job?
Let the cashier hours be c. Let the tutor hours be t. We're given 2 equations:
[LIST=1]
[*]c + t = 30
[*]8c + 12t = 268
[/LIST]
To solve this system of equations, we can use 3 methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+t+%3D+30&term2=8c+%2B+12t+%3D+268&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+t+%3D+30&term2=8c+%2B+12t+%3D+268&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+t+%3D+30&term2=8c+%2B+12t+%3D+268&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we use, we get the same answer:
[LIST]
[*]c = [B]23[/B]
[*]t = [B]7[/B]
[/LIST]
Parallel ResistorsFree Parallel Resistors Calculator - Given a set of parallel resistors, this calculates the total resistance in ohms, denoted Rt
Payback PeriodFree Payback Period Calculator - Given a set of cash inflows and cash outflows at certain times, this determines the net cash flow, cumulative cash flow, and payback period
PentagonsFree Pentagons Calculator - Given a side length and an apothem, this calculates the perimeter and area of the pentagon.
Percent Off ProblemFree Percent Off Problem Calculator - Given the 3 items of a percent word problem, Reduced Price, percent off, and full price, this solves for any one of the three given two of the items.
Percentage AppreciationFree Percentage Appreciation Calculator - Solves for Book Value given a flat rate percentage appreciation per period
Percentage DepreciationFree Percentage Depreciation Calculator - Solves for Book Value given a flat rate percentage depreciation per period
Percentage of CompletionFree Percentage of Completion Calculator - Given a sales price, total costs, and costs per period, this determines the gross profit to date using the percentage of completion method.
Percentile for Normal DistributionFree Percentile for Normal Distribution Calculator - Given a mean, standard deviation, and a percentile range, this will calculate the percentile value.
PercentilesFree Percentiles Calculator - Given a set of scores and a target score, this will determine the percentile of the target score using two different formulas.
Perimeter of a rectangle is 372 yards. If the length is 99 yards, what is the width?Perimeter of a rectangle is 372 yards. If the length is 99 yards, what is the width?
The perimeter P of a rectangle with length l and width w is:
2l + 2w = P
We're given P = 372 and l = 99, so we have:
2(99) + 2w = 372
2w + 198 = 372
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 198 and 372. To do that, we subtract 198 from both sides
2w + 198 - 198 = 372 - 198
[SIZE=5][B]Step 2: Cancel 198 on the left side:[/B][/SIZE]
2w = 174
[SIZE=5][B]Step 3: Divide each side of the equation by 2[/B][/SIZE]
2w/2 = 174/2
w = [B]87[/B]
Peter is buying office supplies. He is able to buy 3 packages of paper and 4 staplers for $40, or hePeter is buying office supplies. He is able to buy 3 packages of paper and 4 staplers for $40, or he is able to buy 5 packages of paper and 6 staplers for $62. How much does a package of paper cost? How much does a stapler cost?
Let the cost of paper packages be p and the cost of staplers be s. We're given two equations:
[LIST=1]
[*]3p + 4s = 40
[*]5p + 6s = 62
[/LIST]
We have a system of equations. We can solve this three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3p+%2B+4s+%3D+40&term2=5p+%2B+6s+%3D+62&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3p+%2B+4s+%3D+40&term2=5p+%2B+6s+%3D+62&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3p+%2B+4s+%3D+40&term2=5p+%2B+6s+%3D+62&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we choose, we get the same answer:
[LIST]
[*][B]p = 4[/B]
[*][B]s = 7[/B]
[/LIST]
Phone Number TranslatorFree Phone Number Translator Calculator - Given a phone number with letters in it, this calculator will determine the numeric phone number for you to dial.
Phonetic AlgorithmsFree Phonetic Algorithms Calculator - Given a name, this calculator translates a name to one of the following 3 phonetic algorithms:
* Soundex
* Metaphone
* New York State Identification and Intelligence System (NYSIIS)
Place ValueFree Place Value Calculator - Given a whole number or a decimal, the calculator will perform place number analysis on each place in your number.
For the whole and decimal portion, the calculator goes out to the 100 trillion mark.
Plane and Parametric Equations in R3Free Plane and Parametric Equations in R3 Calculator - Given a vector A and a point (x,y,z), this will calculate the following items:
1) Plane Equation passing through (x,y,z) perpendicular to A
2) Parametric Equations of the Line L passing through the point (x,y,z) parallel to A
Point Estimate and Margin of ErrorFree Point Estimate and Margin of Error Calculator - Given an upper bound and a lower bound and a sample size, this calculate the point estimate, margin of error.
Polar ConicsFree Polar Conics Calculator - Given eccentricity (e), directrix (d), and angle θ, this determines the vertical and horizontal directrix polar equations.
Polygon SideFree Polygon Side Calculator - Determines the sides of a polygon given an interior angle sum.
Pool VolumeFree Pool Volume Calculator - Given a round shaped pool, this calculates the volume (Capacity) in gallons of the pool when filled with water
Portfolio Rate of ReturnFree Portfolio Rate of Return Calculator - Given a portfolio of individual assets with returns and weights, this calculates the total portfolio rate of return.
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PredecessorFree Predecessor Calculator - Calculates the predecessor number to a given number
PriceFree Price Calculator - Given a cost and a gross margin percentage, this calculator calculates price, gross profit, markup percentage
Primitive RootFree Primitive Root Calculator - Given a prime number p and a potential root of b, this determines if b is a primitive root of p.
Probability (A U B)Free Probability (A U B) Calculator - Given a 2 event sample space A and B, this calculates the probability of the following events:
P(A U B)
P(A)
P(B)
P(A ∩ B)
Problems Involving Rational ExpressionsWe are given, using the word word problem combined formula, that:
1/j + 1/p + 1/m = 1/3
However, you state the hours working alone, but then ask how much it would take working alone. I'm confused on the last part. Can you clarify?
Q is a point on segment PR. If PQ = 2.7 and PR = 6.1, what is QR?Q is a point on segment PR. If PQ = 2.7 and PR = 6.1, what is QR?
From segment addition, we know that:
PQ + QR = PR
Plugging our given numbers in, we get:
2.7 + QR = 6.1
Subtract 2.7 from each side, and we get:
2.7 - 2.7 + QR = 6.1 - 2.7
Cancelling the 2.7 on the left side, we get:
QR = [B]3.4[/B]
QuadrilateralFree Quadrilateral Calculator - Given 4 points entered, this determines the area using Brahmaguptas Formula and perimeter of the quadrilateral formed by the points as well as checking to see if the quadrilateral (quadrangle) is a parallelogram.
Quotient-Remainder TheoremFree Quotient-Remainder Theorem Calculator - Given 2 positive integers n and d, this displays the quotient remainder theorem.
Rachel works at a bookstore. On Tuesday, she sold twice as many books as she did on Monday. On WedneRachel works at a bookstore. On Tuesday, she sold twice as many books as she did on Monday. On Wednesday, she sold 6 fewer books than she did on Tuesday. During the 3 days Rachel sold 19 books. Create an equation that can be used to find m, a number of books Rachel sold on Monday.
Let me be the number of books Rachel sold on Monday. We're given Tuesday's book sales (t) and Wednesday's books sales (w) as:
[LIST=1]
[*]t = 2m
[*]w = t - 6
[*]m + t + w = 19
[/LIST]
Plug (1) and (2) into (3):
Since t = 2m and w = t - 6 --> 2m - 6, we have:
m + 2m + 2m - 6 = 19
Combine like terms:
5m - 6 = 19
[URL='https://www.mathcelebrity.com/1unk.php?num=5m-6%3D19&pl=Solve']Plugging this equation into our search engine[/URL], we get:
[B]m = 5[/B]
Random TestFree Random Test Calculator - Given a set of data and an α value, this determines the test statistic and accept/reject hypothesis based on randomness of a dataset.
Rates of ReturnFree Rates of Return Calculator - Given a set of stock prices and dividends if applicable, this calculates the periodic rate of return and the logarithmic rate of return
Ratio Word ProblemsFree Ratio Word Problems Calculator - Solves a ratio word problem using a given ratio of 2 items in proportion to a whole number.
RatiosFree Ratios Calculator - * Simplifies a ratio of a:b
* Given a ratio in the form a:b or a to b, and a total population amount, this calculator will determine the expected value of A and B from the ratio.
Ravi deposits $500 into an account that pays simple interest at a rate of 4% per year. How much inteRavi deposits $500 into an account that pays simple interest at a rate of 4% per year. How much interest will he be paid in the first 4 years?
The formula for [U]interest[/U] using simple interest is:
I = Prt where P = Principal, r = interest, and t = time.
We're given P = 500, r =0.04, and t = 4. So we plug this in and get:
I = 500(0.04)(4)
I = [B]80[/B]
Rebound RatioFree Rebound Ratio Calculator - Calculates a total downward distance traveled given an initial height of a drop and a rebound ratio percentage
Receivables RatiosFree Receivables Ratios Calculator - Given Net Sales, Beginning Accounts Receivable, and Ending Accounts Receivable, this determines Average Accounts Receivable, Receivables turnover ratio, and Average Collection Period.
rectangle abcd prove: triangle adc is congruent to triangle bcdrectangle abcd prove: triangle adc is congruent to triangle bcd
1. Given: ABCD is a rectangle
2. AB = CD since opposite sides of rectangle are congruent
3. BC = AD since opposite sides of rectangle are congruent
4. AC = AC by the Reflexive Property of Equality
5. triangle ADC = triangle CBA by the Side-Side-Side (SSS) Property
Reference AngleFree Reference Angle Calculator - Calculates the reference angle for a given angle. Also known as the positive acute angle.
Relative CoordinatesFree Relative Coordinates Calculator - Given a starting point (x1,y1), this will determine your relative coordinates after moving up, down, left, and right.
Resistor Color CodesFree Resistor Color Codes Calculator - Given 3 Band level color codes and a tolerance color chosen, this calculates the resistance in ohms and the tolerance percentage
RhombusFree Rhombus Calculator - Given inputs of a rhombus, this calculates the following:
Perimeter of a Rhombus
Area of a Rhombus
Side of a Rhombus
Rico was born 6 years after Nico. The sum of their age is 36. How old is Nico?Rico was born 6 years after Nico. The sum of their age is 36. How old is Nico?
Let Rico's age be r
Let Nico's age be n
We're given two equations:
[LIST=1]
[*]r = n + 6
[*]n + r = 36
[/LIST]
We plug equation (1) into equation (2) for r:
n + n + 6 = 36
To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n%2Bn%2B6%3D36&pl=Solve']type it in our search engine[/URL] and we get:
[B]n = 15[/B]
Rigby and Eleanor's combined score on the systems of equations test was 181. Rigby scored 9 more poiRigby and Eleanor's combined score on the systems of equations test was 181. Rigby scored 9 more points than Eleanor. What were Eleanor and Rigby's scores?
Let Rigby's score be r
Let Eleanor's score be e
We're given two equations:
[LIST=1]
[*]r = e + 9
[*]e + r = 181
[/LIST]
Substitute equation (1) into equation (2):
e + (e + 9) = 181
Group like terms:
2e + 9 = 181
To solve this equation for e, we [URL='https://www.mathcelebrity.com/1unk.php?num=2e%2B9%3D181&pl=Solve']type it in our search engine[/URL] and we get:
e = [B]86[/B]
Right TrianglesFree Right Triangles Calculator - This solves for all the pieces of a right triangle based on given inputs using items like the sin ratio, cosine ratio, tangent ratio, and the Pythagorean Theorem as well as the inradius.
Roster NotationFree Roster Notation Calculator - Given a set of numbers, this displays the roster notation
Rule of SuccessionFree Rule of Succession Calculator - Given s successes in n independent trials, this calculates the probability that the next repetition is a success
Run Length EncodingFree Run Length Encoding Calculator - Given a string, this will determine the run length encoding using repeating patterns of characters.
Sadie and Connor both play soccer. Connor scored 2 times as many goals as Sadie. Together they scoreSadie and Connor both play soccer. Connor scored 2 times as many goals as Sadie. Together they scored 9 goals. Could Sadie have scored 4 goals? Why or why not?
[U]Assumptions:[/U]
[LIST]
[*]Let Connor's goals be c
[*]Let Sadie's goals be s
[/LIST]
We're given the following simultaneous equations:
[LIST=1]
[*]c = 2s
[*]c + s = 9
[/LIST]
We substitute equation (1) into equation (2) for c:
2s + s = 9
To solve the equation for s, we type it in our search equation and we get:
s = [B]3[/B]
So [U][B]no[/B][/U], Sadie could not have scored 4 goals since s = 3
sales 45,000 commission rate is 3.6% and salary is $275sales 45,000 commission rate is 3.6% and salary is $275
Set up the commission function C(s) where s is the salary:
C(s) = Commission * s + salary
We're given: C(s) = 45,000, commission = 3.6%, which is 0.036 and salary = 275, so we have:
0.036s + 275 = 45000
To solve for s, we type this equation into our search engine and we get:
s = [B]1,242,361.11[/B]
Sales TaxFree Sales Tax Calculator - Given a sales price and a total bill, this calculates the sales tax amount and sales tax percentage
Sally and Adam works a different job. Sally makes $5 per hour and Adam makes $4 per hour. They eachSally and Adam works a different job. Sally makes $5 per hour and Adam makes $4 per hour. They each earn the same amount per week but Adam works 2 more hours. How many hours a week does Adam work?
[LIST]
[*]Let [I]s[/I] be the number of hours Sally works every week.
[*]Let [I]a[/I] be the number of hours Adam works every week.
[*]We are given: a = s + 2
[/LIST]
Sally's weekly earnings: 5s
Adam's weekly earnings: 4a
Since they both earn the same amount each week, we set Sally's earnings equal to Adam's earnings:
5s = 4a
But remember, we're given a = s + 2, so we substitute this into Adam's earnings:
5s = 4(s + 2)
Multiply through on the right side:
5s = 4s + 8 <-- [URL='https://www.mathcelebrity.com/expand.php?term1=4%28s%2B2%29&pl=Expand']multiplying 4(s + 2)[/URL]
[URL='https://www.mathcelebrity.com/1unk.php?num=5s%3D4s%2B8&pl=Solve']Typing this equation into the search engine[/URL], we get s = 8.
The problem asks for Adam's earnings (a). We plug s = 8 into Adam's weekly hours:
a = s + 2
a = 8 + 2
[B]a = 10[/B]
Sally earns $19.25 per hour. This week she earned $616. Write a two step equation to represent the pSally earns $19.25 per hour. This week she earned $616. Write a two step equation to represent the problem
Let hours be h. We're given:
[B]19.25h = 616[/B]
Sally found 73 seashells on the beach, she gave Mary some of her seashells. She has 10 left. How manSally found 73 seashells on the beach, she gave Mary some of her seashells. She has 10 left. How many did she give to Mary?
Let the number of seashells Sally gave away as g. We're given:
73 - g = 10
To solve this equation for g, we [URL='https://www.mathcelebrity.com/1unk.php?num=73-g%3D10&pl=Solve']type it in our search engine[/URL] and we get:
g = [B]63[/B]
Sally is 4 years older than Mark. Twice Sally's age plus 5 times Mark's age is equal to 64.Sally is 4 years older than Mark. Twice Sally's age plus 5 times Mark's age is equal to 64.
Let Sally's age be s. Let Mark's age be m. We're given two equations:
[LIST=1]
[*]s = m + 4
[*]2s + 5m = 64 <-- [I]Since Twice means we multiply by 2[/I]
[/LIST]
Substitute equation (1) into equation (2):
2(m + 4) + 5m = 64
Multiply through:
2m + 8 + 5m = 64
Group like terms:
(2 + 5)m + 8 = 64
7m + 8 = 64
[URL='https://www.mathcelebrity.com/1unk.php?num=7m%2B8%3D64&pl=Solve']Type this equation into the search engine[/URL] and we get:
m = [B]8[/B]
Sam and Jeremy have ages that are consecutive odd integers. The product of their ages is 783. WhichSam and Jeremy have ages that are consecutive odd integers. The product of their ages is 783. Which equation could be used to find Jeremy's age, j, if he is the younger man.
Let Sam's age be s. Let' Jeremy's age be j. We're given:
[LIST=1]
[*]s = j + 2 <-- consecutive odd integers
[*]sj = 783
[/LIST]
Substitute (1) into (2):
(j + 2)j = 783
j^2 + 2j = 783
Subtract 783 from each side:
j^2 + 2j - 783 = 0 <-- This is the equation to find Jeremy's age.
To solve this, [URL='https://www.mathcelebrity.com/quadratic.php?num=j%5E2%2B2j-783%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']we type this quadratic equation into the search engine[/URL] and get:
j = 27, j = -29.
Since ages cannot be negative, we have:
[B]j = 27[/B]
Sam has $2.25 in quarters and dimes, and the total number of coins is 12. How many quarters and howSam has $2.25 in quarters and dimes, and the total number of coins is 12. How many quarters and how many dimes?
Let d be the number of dimes. Let q be the number of quarters. We're given two equations:
[LIST=1]
[*]0.1d + 0.25q = 2.25
[*]d + q = 12
[/LIST]
We have a simultaneous system of equations. We can solve this 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.1d+%2B+0.25q+%3D+2.25&term2=d+%2B+q+%3D+12&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.1d+%2B+0.25q+%3D+2.25&term2=d+%2B+q+%3D+12&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.1d+%2B+0.25q+%3D+2.25&term2=d+%2B+q+%3D+12&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
[LIST]
[*][B]d = 5[/B]
[*][B]q = 7[/B]
[/LIST]
Sam is 52 years old. This is 20 years less than 3 times the age of John. How old is JohnSam is 52 years old. This is 20 years less than 3 times the age of John. How old is John
Let John's age be j. We're given the following equation:
3j - 20 = 52 ([I]Less than[/I] means we subtract)
To solve for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=3j-20%3D52&pl=Solve']type this equation into our search engine[/URL] and we get:
j = [B]24[/B]
Sample Size Reliability for μFree Sample Size Reliability for μ Calculator - Given a population standard deviation σ, a reliability (confidence) value or percentage, and a variation, this will calculate the sample size necessary to make that test valid.
Sample Size Requirement for the Difference of MeansFree Sample Size Requirement for the Difference of Means Calculator - Given a population standard deviation 1 of σ1, a population standard deviation 2 of σ2 a reliability (confidence) value or percentage, and a variation, this will calculate the sample size necessary to make that test valid.
Sample Space ProbabilityFree Sample Space Probability Calculator - Given a sample space S and an Event Set E, this calculates the probability of the event set occuring.
SequencesFree Sequences Calculator - Given a function a(n) and a count of sequential terms you want to expand (n), this calcuator will determine the first (n) terms of your sequence, {a1, a2, ..., an}
Set NotationFree Set Notation Calculator - Given two number sets A and B, this determines the following:
* Union of A and B, denoted A U B
* Intersection of A and B, denoted A ∩ B
* Elements in A not in B, denoted A - B
* Elements in B not in A, denoted B - A
* Symmetric Difference A Δ B
* The Concatenation A · B
* The Cartesian Product A x B
* Cardinality of A = |A|
* Cardinality of B = |B|
* Jaccard Index J(A,B)
* Jaccard Distance Jσ(A,B)
* Dice's Coefficient
* If A is a subset of B
* If B is a subset of A
Set of 2 digit even numbers less than 40Set of 2 digit even numbers less than 40
Knowns and givens:
[LIST]
[*]2 digit numbers start at 10
[*]Less than 40 means we do not include 40
[*]Even numbers are divisible by 2
[/LIST]
[B]{10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38}[/B]
Shalini gave 0.4 of her plums to her brother and 20% to her sister. She kept 16 for herself how manyShalini gave 0.4 of her plums to her brother and 20% to her sister. She kept 16 for herself how many plums did she have at first?
Let p be the number of plums Shalini started with. We have:
[LIST]
[*]0.4 given to her brother
[*]20% which is 0.2 given away to her sister
[*]What this means is she kept 1 - (0.4 + 0.2) = 1 - 0.6 = 0.4 for herself
[/LIST]
0.4p = 16
Divide each side by 0.4
[B]p = 40[/B]
Sharpe RatioFree Sharpe Ratio Calculator - Calculates the Sharpe ratio given return on assets, risk free rate, and standard deviation
She earns $20 per hour as a carpenter and $25 per hour as a blacksmith, last week Giselle worked botShe earns $20 per hour as a carpenter and $25 per hour as a blacksmith, last week Giselle worked both jobs for a total of 30 hours, and a total of $690. How long did Giselle work as a carpenter and how long did she work as a blacksmith?
Assumptions:
[LIST]
[*]Let b be the number of hours Giselle worked as a blacksmith
[*]Let c be the number of hours Giselle worked as a carpenter
[/LIST]
Givens:
[LIST=1]
[*]b + c = 30
[*]25b + 20c = 690
[/LIST]
Rearrange equation (1) to solve for b by subtracting c from each side:
[LIST=1]
[*]b = 30 - c
[*]25b + 20c = 690
[/LIST]
Substitute equation (1) into equation (2) for b
25(30 - c) + 20c = 690
Multiply through:
750 - 25c + 20c = 690
To solve for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=750-25c%2B20c%3D690&pl=Solve']type this equation into our search engine[/URL] and we get:
c = [B]12
[/B]
Now, we plug in c = 12 into modified equation (1) to solve for b:
b = 30 - 12
b = [B]18[/B]
Sherry is 31 years younger than her mom. The sum of their ages is 61. How old is Sherry?Sherry is 31 years younger than her mom. The sum of their ages is 61. How old is Sherry?
Let Sherry's age be s. Let the mom's age be m. We're given two equations:
[LIST=1]
[*]s = m - 31
[*]m + s = 61
[/LIST]
Substitute equation (1) into equation (2) for s:
m + m - 31 = 61
To solve for m, [URL='https://www.mathcelebrity.com/1unk.php?num=m%2Bm-31%3D61&pl=Solve']we type this equation into our search engine[/URL] and we get:
m = 46
Now, we plug m = 46 into equation (1) to find Sherry's age s:
s = 46 - 31
s = [B]15[/B]
Sigmoid FunctionFree Sigmoid Function Calculator - Calculates the Sigmoid Function S(x) given an x value
Simple Discount and Compound DiscountFree Simple Discount and Compound Discount Calculator - Given a principal value, interest rate, and time, this calculates the Accumulated Value using Simple Discount and Compound Discount
Sine WaveFree Sine Wave Calculator - Solves for any of the 3 items of the Sine Wave: Peak Value, Average Value, and RMS value given 1 input.
Small pizzas were $3 and large pizzas were $5. To feed the throng, it was necessary to spend $475 foSmall pizzas were $3 and large pizzas were $5. To feed the throng, it was necessary to spend $475 for 125 pizzas. How many small pizzas were purchased?
Let s be the number of small pizzas and l be the number of large pizzas. We have two given equations:
[LIST=1]
[*]l + s = 125
[*]3s + 5l = 475
[/LIST]
Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=l+%2B+s+%3D+125&term2=3s+%2B+5l+%3D+475&pl=Cramers+Method']simultaneous equation calculator[/URL], we get [B]s = 75[/B]:
Solution MixtureFree Solution Mixture Calculator - Determines a necessary amount of a Solution given two solution percentages and 1 solution amount.
Some History teachers at Richmond High School are purchasing tickets for students and their adult chSome History teachers at Richmond High School are purchasing tickets for students and their adult chaperones to go on a field trip to a nearby museum. For her class, Mrs. Yang bought 30 student tickets and 30 adult tickets, which cost a total of $750. Mr. Alexander spent $682, getting 28 student tickets and 27 adult tickets. What is the price for each type of ticket?
Let the number of adult tickets be a
Let the number of student tickets be s
We're given two equations:
[LIST=1]
[*]30a + 30s = 750
[*]27a + 28s = 682
[/LIST]
To solve the simultaneous equations, we can use any of three methods below:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=30a+%2B+30s+%3D+750&term2=27a+%2B+28s+%3D+682&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=30a+%2B+30s+%3D+750&term2=27a+%2B+28s+%3D+682&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=30a+%2B+30s+%3D+750&term2=27a+%2B+28s+%3D+682&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we use, we get the same answers:
[LIST]
[*][B]a = 18[/B]
[*][B]s = 7[/B]
[/LIST]
Sophie and Claire are having a foot race. Claire is given a 100-foot head-start. If Sophie is runnSophie and Claire are having a foot race. Claire is given a 100-foot head-start. If Sophie is running at 5 feet per second and Claire is running at 3 feet per second.
i. After how many seconds will Sophie catch Claire?
ii. If the race is 500 feet, who wins?
i.
Sophie's distance formula is given as D = 5s
Claire's distance formula is given as D = 3s + 100
Set them equal to each other
5s = 3s + 100
Subtract 3s from both sides:
2s = 100
Divide each side by 2
[B]s = 50[/B]
ii. [B]Sophie since after 50 seconds, she takes the lead and never gives it back.[/B]
Special Triangles: Isosceles and 30-60-90Free Special Triangles: Isosceles and 30-60-90 Calculator - Given an Isosceles triangle (45-45-90) or 30-60-90 right triangle, the calculator will solve the 2 remaining sides of the triangle given one side entered.
spent $19.05. ended with $7.45. how much did you start with?spent $19.05. ended with $7.45. how much did you start with?
Let s be the amount we started with. We're given:
s - 19.05 = 7.45
To solve this equation for s, we t[URL='https://www.mathcelebrity.com/1unk.php?num=s-19.05%3D7.45&pl=Solve']ype it in our math engine [/URL]and we get:
[B]s = 26.5[/B]
Split Fund InterestFree Split Fund Interest Calculator - Given an initial principal amount, interest rate on Fund 1, interest rate on Fund 2, and a total interest paid, calculates the amount invested in each fund.
Square Roots and ExponentsFree Square Roots and Exponents Calculator - Given a number (n), or a fraction (n/m), and/or an exponent (x), or product of up to 5 radicals, this determines the following:
* The square root of n denoted as √n
* The square root of the fraction n/m denoted as √n/m
* n raised to the xth power denoted as nx (Write without exponents)
* n raised to the xth power raised to the yth power denoted as (nx)y (Write without exponents)
* Product of up to 5 square roots: √a√b√c√d√e
* Write a numeric expression such as 8x8x8x8x8 in exponential form
Standard Normal DistributionFree Standard Normal Distribution Calculator - Givena normal distribution z-score critical value, this will generate the probability. Uses the NORMSDIST Excel function.
Stanley bought a ruler and a yardstick for $1.25. If the yardstick cost 45 cents more than the rulerStanley bought a ruler and a yardstick for $1.25. If the yardstick cost 45 cents more than the ruler, what was the cost of the yardstick?
Let r be the cost of the ruler
Let y be the cost of the yardstick
We're given 2 equations:
[LIST=1]
[*]r + y = 1.25
[*]y = r + 0.45
[/LIST]
Substitute equation (2) into equation (1) for y
r + r + 0.45 = 1.25
Solve for [I]r[/I] in the equation r + r + 0.45 = 1.25
[SIZE=5][B]Step 1: Group the r terms on the left hand side:[/B][/SIZE]
(1 + 1)r = 2r
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
2r + 0.45 = + 1.25
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 0.45 and 1.25. To do that, we subtract 0.45 from both sides
2r + 0.45 - 0.45 = 1.25 - 0.45
[SIZE=5][B]Step 4: Cancel 0.45 on the left side:[/B][/SIZE]
2r = 0.8
[SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE]
2r/2 = 0.8/2
r = 0.4
Substitute r = 0.4 into equation (2) above:
y = r + 0.45
y = 0.4 + 0.45
r = [B]0.85
[URL='https://www.mathcelebrity.com/1unk.php?num=r%2Br%2B0.45%3D1.25&pl=Solve']Source[/URL][/B]
Static Determinacy and StabilityFree Static Determinacy and Stability Calculator - Given a number of joints (j) and a number of members (m), this determines if a truss is statically determinate, statically indeterminate, or unstable
Steven has some money. If he spends $9, then he will have 3/5 of the amount he started with.Steven has some money. If he spends $9, then he will have 3/5 of the amount he started with.
Let the amount Steven started with be s. We're given:
s - 9 = 3s/5
Multiply each side through by 5 to eliminate the fraction:
5(s - 9) = 5(3s/5)
Cancel the 5's on the right side and we get:
5s - 45 = 3s
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=5s-45%3D3s&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]22.5[/B]
Stopping-Braking Distance for a CarFree Stopping-Braking Distance for a Car Calculator - Calculates the estimated stopping distance of a vehicle given a speed in miles per hour (mph)
String Comparison AlgorithmsFree String Comparison Algorithms Calculator - Given two strings A and B, this calculates the following items:
1) Similar Text Pair Ranking Score
2) Levenshtein (Edit Distance).
Student-t Distribution Critical ValuesFree Student-t Distribution Critical Values Calculator - Given an α value and degrees of freedom, this calculates the right-tailed test and left-tailed test critical values for the Student-t Distribution
Substitute the given values into given formula and solve for the unknown variable. S=4LW + 2 WH; S=Substitute the given values into given formula and solve for the unknown variable. S = 4LW + 2 WH; S= 144, L= 8, W= 4. H=
S = 4LW + 2 WH
Substituting our given values, we have:
144 = 4(8)(4) + 2(4)H
144 = 128 + 8H
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=128%2B8h%3D144&pl=Solve']equation calculator[/URL], we get:
[B]H = 2[/B]
SuccessorFree Successor Calculator - Calculates the successor number to a given number
Sum to Product and Product to Sum FormulasFree Sum to Product and Product to Sum Formulas Calculator - Given two angles in degrees of u and v, this determines the following:
* Sin(u) ± Sin(v)
* Cos(u) ± Cos(v)
* Sin(u)Sin(v)
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* Cos(u)Sin(v)
* Sin(u + v)
* Sin(u - v)
* Cos(u + v)
* Cos(u - v)
* Tan(u + v)
* Tan(u - v)
Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gaSuppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 20 gallons of fuel, the airplane weighs 2012 pounds. When carrying 55 gallons of fuel, it weighs 2208 pounds. How much does the airplane weigh if it is carrying 65 gallons of fuel?
Linear functions are written in the form of one dependent variable and one independent variable. Using g as the number of gallons and W(g) as the weight, we have:
W(g) = gx + c where c is a constant
We are given:
[LIST]
[*]W(20) = 2012
[*]W(55) = 2208
[/LIST]
We want to know W(65)
Using our givens, we have:
W(20) = 20x + c = 2012
W(55) = 55x + c = 2208
Rearranging both equations, we have:
c = 2012 - 20x
c = 2208 - 55x
Set them both equal to each other:
2012 - 20x = 2208 - 55x
Add 55x to each side:
35x + 2012 = 2208
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=35x%2B2012%3D2208&pl=Solve']equation solver[/URL], we see that x is 5.6
Plugging x = 5.6 back into the first equation, we get:
c = 2012 - 20(5.6)
c = 2012 - 112
c = 2900
Now that we have all our pieces, find W(65)
W(65) = 65(5.6) + 2900
W(65) = 264 + 2900
W(65) = [B]3264[/B]
Survival RatesFree Survival Rates Calculator - Given a set of times and survival population counts, the calculator will determine the following:
Survival Population lx
Mortality Population dx
Survival Probability px
Mortality Probability qx
In addition, the calculator will determine the probability of survival from tx to tx + n
Susan works as a tutor for $14 an hour and as a waitress for $13 an hour. This month, she worked a cSusan works as a tutor for $14 an hour and as a waitress for $13 an hour. This month, she worked a combined total of 104 hours at her two jobs. Let t be the number of hours Susan worked as a tutor this month. Write an expression for the combined total dollar amount she earned this month.
Let t be the number of hours for math tutoring and w be the number of hours for waitressing. We're given:
[LIST=1]
[*]t + w = 104
[*]14t + 13w = D <-- Combined total dollar amount
[/LIST]
tammy earns $18000 salary with 4% comission on sales. How much should she sell to earn $55,000 totaltammy earns $18000 salary with 4% comission on sales. How much should she sell to earn $55,000 total
We have a commission equation below:
Sales * Commission percent = Salary
We're given 4% commission percent and 55,000 salary. With 4% as 0.04, we have:
Sales * 0.04 = 55,000
Divide each side of the equation by 0.04, and we get:
Sales = [B]1,375,000[/B]
Target Heart RateFree Target Heart Rate Calculator - Given an age, this calculator determines the following 5 target heart rate zones:
Healthy Heart Zone (Warm up) 50 - 60%
Fitness Zone (Fat Burning) 60 - 70%
Aerobic Zone (Endurance Training) 70 - 80%
Anaerobic Zone (Performance Training) 80 - 90%
Red Line (Maximum Effort) 90 - 100%
The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 32The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 327 people entered the park , and the admission fee collected totaled 978.00 dollars . How many children and how many adults were admitted?
Let the number of children's tickets be c. Let the number of adult tickets be a. We're given two equations:
[LIST=1]
[*]a + c = 327
[*]4a + 1.50c = 978
[/LIST]
We can solve this system of equation 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+327&term2=4a+%2B+1.50c+%3D+978&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+327&term2=4a+%2B+1.50c+%3D+978&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+327&term2=4a+%2B+1.50c+%3D+978&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answers:
[LIST]
[*][B]a = 195[/B]
[*][B]c = 132[/B]
[/LIST]
The average cost of printing a book in a publishing company is c(x) = 5.5x+kx , where x is the numbeThe average cost of printing a book in a publishing company is c(x) = 5.5x+kx , where x is the number of books printed that day and k is a constant. Find k, if on the day when 200 were printed the average cost was $9 per book.
We are given: c(200) = 9, so we have:
9 = 5.5(200) + k(200)
200k + 1100 = 9
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=200k%2B1100%3D9&pl=Solve']equation solver[/URL], we get:
[B]k = -5.455[/B]
The average height of a family of 6 is 6 feet. After the demise of the mother, the average height reThe average height of a family of 6 is 6 feet. After the demise of the mother, the average height remained the same. What is the height of the mother?
[LIST]
[*]Let the height of the family without the mom be f. Let the height of the mother be m.
[*]Averages mean we add the heights and divide by the number of people who were measured.
[/LIST]
We're given two equations:
[LIST=1]
[*](f + m)/6 = 6
[*]f/5 = 6
[/LIST]
Cross multiplying equation (2), we get:
f = 5 * 6
f = 30
Plug f = 30 into equation (1), we get:
(30 + m)/6 = 6
Cross multiplying, we get:
m + 30 = 6 * 6
m + 30 = 36
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B30%3D36&pl=Solve']type it in our search engine[/URL] and we get:
m = [B]6[/B]
[SIZE=3][FONT=Arial][COLOR=rgb(34, 34, 34)][/COLOR][/FONT][/SIZE]
The base of a triangle with a height of 7 units is represented by the formula b=2/7A. The base of thThe base of a triangle with a height of 7 units is represented by the formula b=2/7A. The base of the triangle is less than 10 units. Write and solve an inequality that represents the possible area A of the triangle
We're given:
b=2/7A
We're also told that b is less than 10. So we have:
2/7A < 10
2A/7 < 10
Cross multiply:
2A < 7 * 10
2A < 70
Divide each side of the inequality by 2 to isolate A
2A/2 < 70/2
Cancel the 2's on the left side and we get:
A < [B]35[/B]
The bigger of 2 numbers in 5 larger than the smaller. Twice the smaller, increased by, twice the larThe bigger of 2 numbers in 5 larger than the smaller. Twice the smaller, increased by, twice the larger, is equal to 50. Find each number.
Let the big number be b. Let the small number be s. We're given two equations:
[LIST=1]
[*]b = s + 5
[*]2s + 2b = 50
[/LIST]
Substitute equation (1) into equation (2)
2s + 2(s + 5) = 50
[URL='https://www.mathcelebrity.com/1unk.php?num=2s%2B2%28s%2B5%29%3D50&pl=Solve']Type this equation into our search engine[/URL], and we get:
[B]s = 10[/B]
Now substitute s = 10 into equation (1) to solve for b:
b = 10 + 5
[B]b = 15[/B]
The cost of 25 apples is less than $9.50. The cost of 12 apples is more than 3.60. What are the possThe cost of 25 apples is less than $9.50. The cost of 12 apples is more than 3.60. What are the possible prices of one apple?
Let a be the price of each apple. We're given 2 inequalities:
[LIST=1]
[*]25a < 9.50
[*]12a > 3.60
[/LIST]
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=25a%3C9.50&pl=Show+Interval+Notation']Typing 25a < 9.50 into our search engine[/URL], we get a < 0.38
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=12a%3E3.60&pl=Show+Interval+Notation']Typing 12a > 360 into our search engine[/URL], we get a > 0.3
Therefore, the possible prices a of one apple are expressed as the inequality:
[B]0.3 < a < 0.38[/B]
the cost of a buffet at a restaurant is different for adults and kids. the bill for 2 adults and 3 kthe cost of a buffet at a restaurant is different for adults and kids. the bill for 2 adults and 3 kids is $51. the bill for 3 adults and 1 kid is $45. what is the cost per adult and per kid?
Let the cost for each adult be a
Let the cost for each kid be k
We're given two equations:
[LIST=1]
[*]2a + 3k = 51
[*]3a + k = 45
[/LIST]
To solve this simultaneous set of equations, we can use three methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2a+%2B+3k+%3D+51&term2=3a+%2B+k+%3D+45&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2a+%2B+3k+%3D+51&term2=3a+%2B+k+%3D+45&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2a+%2B+3k+%3D+51&term2=3a+%2B+k+%3D+45&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we use, we get the same answer:
[LIST]
[*]a = [B]12[/B]
[*]k = [B]9[/B]
[/LIST]
The cost of a gallon of milk (m) is .50 more than 5 times the cost of a gallon of water (w). If a gaThe cost of a gallon of milk (m) is .50 more than 5 times the cost of a gallon of water (w). If a gallon of milk cost 3.75, what is the cost of a gallon of water?
We're given:
m = 5w + 0.50
m = $3.75
Set them equal to each other:
5w + 0.50 = 3.75
[URL='https://www.mathcelebrity.com/1unk.php?num=5w%2B0.50%3D3.75&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 0.65[/B]
The denominator of a fraction is 4 more than the numerator. If 4 is added to the numerator and 7 isThe denominator of a fraction is 4 more than the numerator. If 4 is added to the numerator and 7 is added to the denominator, the value of the fraction is 1/2. Find the original fraction.
Let the original fraction be n/d.
We're given:
[LIST=1]
[*]d = n + 4
[*](n + 4) / (d + 7) = 1/2
[/LIST]
Cross multiply Equation 2:
2(n + 4) = d + 7
2n + 8 = d + 7
Now substitute equation (1) into tihs:
2n + 8 = (n + 4) + 7
2n + 8 = n + 11
[URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B8%3Dn%2B11&pl=Solve']Type this equation into our search engine[/URL], and we get:
n = 3
This means from equation (1), that:
d = 3 + 4
d = 7
So our original fraction n/d = [B]3/7[/B]
The difference between 2 numbers is 108. 6 times the smaller is equal to 2 more than the larger. Wh?The difference between 2 numbers is 108. 6 times the smaller is equal to 2 more than the larger. What are the numbers?
Let the smaller number be x. Let the larger number be y. We're given:
[LIST=1]
[*]y - x = 108
[*]6x = y + 2
[/LIST]
Rearrange (1) by adding x to each side:
[LIST=1]
[*]y = x + 108
[/LIST]
Substitute this into (2):
6x = x + 108 + 2
Combine like terms
6x = x +110
Subtract x from each side:
5x = 110
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%3D110&pl=Solve']Plugging this equation into our search engine[/URL], we get:
x = [B]22[/B]
The difference between the squares of two consecutive numbers is 141. Find the numbersThe difference between the squares of two consecutive numbers is 141. Find the numbers
Take two consecutive numbers:
n- 1 and n
Given a difference (d) between the squares of two consecutive numbers, the shortcut for this is:
2n - 1 = d
Proof of this:
n^2- (n - 1)^2 = d
n^2 - (n^2 - 2n + 1) = d
n^2 - n^2 + 2n - 1 = d
2n - 1 = d
Given d = 141, we have
2n - 1 = 141
Add 1 to each side:
2n = 142
Divide each side by 2:
2n/2 = 142/2
n = [B]71[/B]
Therefore, n - 1 = [B]70
Our two consecutive numbers are (70, 71)[/B]
Check your work
70^2 = 4900
71^2 = 5041
Difference = 5041 - 4900
Difference = 141
[MEDIA=youtube]vZJtZyYWIFQ[/MEDIA]
The difference between two numbers is 25. The smaller number is 1/6th of the larger number. What isThe difference between two numbers is 25. The smaller number is 1/6th of the larger number. What is the value of the smaller number
Let the smaller number be s. Let the larger number be l. We're given two equations:
[LIST=1]
[*]l - s = 25
[*]s = l/6
[/LIST]
Plug in equation (2) into equation (1):
l - l/6 = 25
Multiply each side of the equation by 6 to remove the fraction:
6l - l = 150
To solve for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=6l-l%3D150&pl=Solve']type this equation into our search engine[/URL] and we get:
l = 30
To solve for s, we plug in l = 30 into equation (2) above:
s = 30/6
[B]s = 5[/B]
The difference between two numbers is 96. One number is 9 times the other. What are the numbers?The difference between two numbers is 96. One number is 9 times the other. What are the numbers?
Let x be the first number
Let y be the second number
We're given two equations:
[LIST=1]
[*]x - y = 96
[*]x = 9y
[/LIST]
Substitute equation (2) into equation (1) for x
9y - y = 96
[URL='https://www.mathcelebrity.com/1unk.php?num=9y-y%3D96&pl=Solve']Plugging this equation into our math engine[/URL], we get:
y = [B]12
[/B]
If y = 12, then we plug this into equation 2:
x = 9(12)
x = [B]108[/B]
The difference of two numbers is 12 and their mean is 15. Find the two numbersThe difference of two numbers is 12 and their mean is 15. Find the two numbers.
Let the two numbers be x and y. We're given:
[LIST=1]
[*]x - y = 12
[*](x + y)/2 = 15. <-- Mean is an average
[/LIST]
Rearrange equation 1 by adding y to each side:
x - y + y = y + 12
Cancelling the y's on the left side, we get:
x = y + 12
Now substitute this into equation 2:
(y + 12 + y)/2 = 15
Cross multiply:
y + 12 + y = 30
Group like terms for y:
2y + 12 = 30
[URL='https://www.mathcelebrity.com/1unk.php?num=2y%2B12%3D30&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]y = 9[/B]
Now substitute this into modified equation 1:
x = y + 12
x = 9 + 12
[B]x = 21[/B]
The difference of two numbers is 720. The smaller of the numbers is 119. What is the other number?The difference of two numbers is 720. The smaller of the numbers is 119. What is the other number?
Let the larger number be l. We're given:
l - 119 = 720
[URL='https://www.mathcelebrity.com/1unk.php?num=l-119%3D720&pl=Solve']We type this equation into the search engine[/URL] and we get:
l = [B]839[/B]
The first group orders 3 pizzas and 4 drinks for $33.50. The second group orders 5 pizzas and 6 drinThe first group orders 3 pizzas and 4 drinks for $33.50. The second group orders 5 pizzas and 6 drinks for $54. Find the cost for each pizza and each drink
Assumptions:
[LIST]
[*]Let the cost of each pizza be p
[*]Let the cost of each drink be d
[/LIST]
Givens:
[LIST=1]
[*]4d + 3p = 33.50
[*]6d + 5p = 54
[/LIST]
We have a simultaneous group of equations. To solve this, we can use 3 methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4d+%2B+3p+%3D+33.50&term2=6d+%2B+5p+%3D+54&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4d+%2B+3p+%3D+33.50&term2=6d+%2B+5p+%3D+54&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4d+%2B+3p+%3D+33.50&term2=6d+%2B+5p+%3D+54&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we use, we get the same answer:
[LIST]
[*]d = [B]$2.75[/B]
[*]p = [B]$7.5[/B]
[/LIST]
The fraction has a value of 3/5. The sum of the numerator and the denominator was 40. What was the fThe fraction has a value of 3/5. The sum of the numerator and the denominator was 40. What was the fraction?
We're given two equations with a fraction with numerator (n) and denominator (d):
[LIST=1]
[*]n + d = 40
[*]n/d = 3/5
[/LIST]
Cross multiply equation 2, we get:
5n = 3d
Divide each side by 5:
5n/5 = 3d/5
n = 3d/5
Substitute this into equation 1:
3d/5 + d = 40
Multiply through both sides of the equation by 5:
5(3d/5) = 5d = 40 * 5
3d + 5d =200
To solve this equation for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=3d%2B5d%3D200&pl=Solve']type it in our search engine and we get[/URL]:
d = [B]25
[/B]
Now substitute that back into equation 1:
n + 25 = 40
Using [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B25%3D40&pl=Solve']our equation solver again[/URL], we get:
n = [B]15[/B]
The Lakers recently scored 81 points. Their points came from 2 and 3 point baskets. If they made 39The Lakers recently scored 81 points. Their points came from 2 and 3 point baskets. If they made 39 baskets total, how many of each basket did they make?
Let x = 2 point baskets and y = 3 point baskets. We have the following given equations:
[LIST=1]
[*]x + y = 39
[*]2x + 3y = 81
[/LIST]
Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=x%2By%3D39&term2=2x+%2B+3y+%3D+81&pl=Cramers+Method']simultaneous equations calculator[/URL], we get:
[B]x = 36 <-- 2 point baskets
y = 3 <-- 3[B] point baskets
[/B][/B]
To confirm our work:
[LIST=1]
[*]36 + 3 = 39
[*]2(36) + 3(3) = 72 + 9 = 81
[/LIST]
The Lakewood library has $8,040 to buy science magazines. If each magazine costs $3, how many magaziThe Lakewood library has $8,040 to buy science magazines. If each magazine costs $3, how many magazines will the library be able to buy?
Let number of magazines be m. We know that:
Cost per magazine * m = Total Cost
We're given Total Cost = 8040 and Cost per magazine = 3, so we have
3m = 8040
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=3m%3D8040&pl=Solve']type it in our math engine[/URL] and we get:
m = [B]2680[/B]
The largest American flag ever flown had a perimeter of 1,520 feet and a length of 505 feet. Find thThe largest American flag ever flown had a perimeter of 1,520 feet and a length of 505 feet. Find the width of the flag.
for a rectangle, the Perimeter P is given by:
P = 2l + 2w
P[URL='https://www.mathcelebrity.com/rectangle.php?l=505&w=&a=&p=1520&pl=Calculate+Rectangle']lugging in our numbers for Perimeter and width into our rectangle calculator[/URL], we get:
l =[B] 255[/B]
The length of a rectangle is 6 less than twice the width. If the perimeter is 60 inches, what are thThe length of a rectangle is 6 less than twice the width. If the perimeter is 60 inches, what are the dimensions?
Set up 2 equations given P = 2l + 2w:
[LIST=1]
[*]l = 2w - 6
[*]2l + 2w = 60
[/LIST]
Substitute (1) into (2) for l:
2(2w - 6) + 2w = 60
4w - 12 + 2w = 60
6w - 12 = 60
To solve for w, [URL='https://www.mathcelebrity.com/1unk.php?num=6w-12%3D60&pl=Solve']type this into our math solver [/URL]and we get:
w = [B]12
[/B]
To solve for l, substitute w = 12 into (1)
l = 2(12) - 6
l = 24 - 6
l = [B]18[/B]
The length of a rectangle is equal to triple the width. Find the length of the rectangle if the periThe length of a rectangle is equal to triple the width. Find the length of the rectangle if the perimeter is 80 inches.
The perimeter (P) of a rectangle is:
2l + 2w = P
We're given two equations:
[LIST=1]
[*]l = 3w
[*]2l + 2w = 80
[/LIST]
We substitute equation 1 into equation 2 for l:
2(3w) + 2w = 80
6w + 2w = 80
To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D80&pl=Solve']type it in our search engine[/URL] and we get:
w = 10
To solve for the length (l), we substitute w = 10 into equation 1 above:
l = 3(10)
l = [B]30[/B]
The length of a rectangle is three times its width.If the perimeter is 80 feet, what are the dimensiThe length of a rectangle is three times its width.If the perimeter is 80 feet, what are the dimensions?
We're given 2 equations:
[LIST=1]
[*]l = 3w
[*]P = 80 = 2l + 2w = 80
[/LIST]
Substitute (1) into (2) for l:
2(3w) + 2w = 80
6w + 2w = 80
8w = 80
Divide each side by 8:
8w/8 = 80/8
w = [B]10
[/B]
Substitute w = 10 into (1)
l = 3(10)
l = [B]30[/B]
The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feeThe length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feet. Find the width and length of the building.
P = 2l + 2w
Since P = 120, we have:
(1) 2l + 2w = 120
We are also given:
(2) l = 3w - 6
Substitute equation (2) into equation (1)
2(3w - 6) + 2w = 120
Multiply through:
6w - 12 + 2w = 120
Combine like terms:
8w - 12 = 120
Add 12 to each side:
8w = 132
Divide each side by 8 to isolate w:
w =16.5
Now substitute w into equation (2)
l = 3(16.5) - 6
l = 49.5 - 6
l = 43.5
So (l, w) = (43.5, 16.5)
The length of a wooden frame is 1 foot longer than its width and its area is equal to 12ft˛The length of a wooden frame is 1 foot longer than its width and its area is equal to 12ft˛
The frame is a rectangle. The area of a rectangle is A = lw. So were given:
[LIST=1]
[*]l = w + 1
[*]lw = 12
[/LIST]
Substitute equation (1) into equation (2) for l:
(w + 1) * w = 12
Multiply through and simplify:
w^2 + w = 12
We have a quadratic equation. To solve for w, we type this equation into our search engine and we get two solutions:
w = 3
w = -4
Since width cannot be negative, we choose the positive result and have:
w = [B]3[/B]
To solve for length, we plug w = 3 into equation (1) above and get:
l = 3 + 1
l = [B]4[/B]
The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her gardenThe length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters. Find the dimensions of Sally’s garden.
Gardens have a rectangle shape. Perimeter of a rectangle is 2l + 2w. We're given:
[LIST=1]
[*]l = 3w + 4 [I](3 times the width Plus 4 since greater means add)[/I]
[*]2l + 2w = 72
[/LIST]
We substitute equation (1) into equation (2) for l:
2(3w + 4) + 2w = 72
Multiply through and simplify:
6w + 8 + 2w = 72
(6 +2)w + 8 = 72
8w + 8 = 72
To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=8w%2B8%3D72&pl=Solve']type it in our search engine[/URL] and we get:
w = [B]8
[/B]
To solve for l, we substitute w = 8 above into Equation (1):
l = 3(8) + 4
l = 24 + 4
l = [B]28[/B]
The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her gardenThe length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters
A garden is a rectangle, which has perimeter P of:
P = 2l + 2w
With P = 72, we have:
2l + 2w = 72
We're also given:
l = 3w + 4
We substitute this into the perimeter equation for l:
2(3w + 4) + 2w = 72
6w + 8 + 2w = 72
To solve this equation for w, we t[URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B8%2B2w%3D72&pl=Solve']ype it in our search engine[/URL] and we get:
w =[B] 8[/B]
Now, to solve for l, we substitute w = 8 into our length equation above:
l = 3(8) + 4
l = 24 + 4
l = [B]28[/B]
The mean age of 5 people in a room is 32 years. A person enters the room. The mean age is now 40. WhThe mean age of 5 people in a room is 32 years. A person enters the room. The mean age is now 40. What is the age of the person who entered the room?
Mean = Sum of Ages in Years / Number of People
32 = Sum of Ages in Years / 5
Cross multiply:
Sum of Ages in Years = 32 * 5
Sum of Ages in Years = 160
Calculate new mean after the next person enters the room.
New Mean = (Sum of Ages in Years + New person's age) / (5 + 1)
Given a new Mean of 40, we have:
40 = (160 + New person's age) / 6
Cross multiply:
New Person's Age + 160 = 40 * 6
New Person's Age + 160 = 240
Let the new person's age be n. We have:
n + 160 = 240
To solve for n, [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B160%3D240&pl=Solve']we type this equation into our search engine[/URL] and we get:
n = [B]80[/B]
The mean age of 5 people in a room is 38 years. A person enters the room. The mean age is now 39. WhThe mean age of 5 people in a room is 38 years. A person enters the room. The mean age is now 39. What is the age of the person who entered the room?
The mean formulas is denoted as:
Mean = Sum of Ages / Total People
We're given Mean = 38 and Total People = 5, so we plug in our numbers:
28 = Sum of Ages / 5
Cross multiply, and we get:
Sum of Ages = 28 * 5
Sum of Ages = 140
One more person enters the room. The mean age is now 39. Set up our Mean formula:
Mean = Sum of Ages / Total People
With a new Mean of 39 and (5 + 1) = 6 people, we have:
39 = Sum of Ages / 6
But the new sum of Ages is the old sum of ages for 5 people plus the new age (a):
Sum of Ages = 140 + a
So we have:
29 = (140 + a)/6
Cross multiply:
140 + a = 29 * 6
140 + a = 174
To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=140%2Ba%3D174&pl=Solve']we type this equation into our search engine[/URL] and we get:
a = [B]34[/B]
the mean of 12 scores is 8.8 . what is the sum of the scores ?the mean of 12 scores is 8.8 . what is the sum of the scores ?
The Mean is denoted as:
Mean = Sum / count
We're given:
8.8 = Sum / 12
Cross multiply and we get:
Sum = 8.8*12
Sum = [B]105.6[/B]
The mean of 3 numbers is 20. Two of the numbers are 21, and 35. What is the 3rd number?The mean of 3 numbers is 20. Two of the numbers are 21, and 35. What is the 3rd number?
The mean of 3 numbers is the sum of 3 numbers divided by 3. Let the 3rd number be n. We have:
Mean = (21 + 35 + n) / 3
The Mean is given as 20, so we have:
20 = (n + 56) / 3
Cross multiply:
n + 56 = 20 * 3
n + 56 = 60
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B56%3D60&pl=Solve']type this number in our search engine [/URL]and we get:
n = [B]4[/B]
The perimeter of a college basketball court is 102 meters and the length is twice as long as the widThe perimeter of a college basketball court is 102 meters and the length is twice as long as the width. What are the length and width?
A basketball court is a rectangle. The perimeter P is:
P = 2l + 2w
We're also given l = 2w and P = 102. Plug these into the perimeter formula:
2(2w) + 2w = 102
4w + 2w = 102
6w = 102
[URL='https://www.mathcelebrity.com/1unk.php?num=6w%3D102&pl=Solve']Typing this equation into our calculator[/URL], we get:
[B]w = 17[/B]
Plug this into the l = 2w formula, we get:
l = 2(17)
[B]l = 34[/B]
The perimeter of a poster is 20 feet. The poster is 6 feet tall. How wide is it?The perimeter of a poster is 20 feet. The poster is 6 feet tall. How wide is it?
[U]Assumptions and givens:[/U]
[LIST]
[*]The poster has a rectangle shape
[*]l = 6
[*]P = 20
[*]The perimeter of a rectangle (P) is: 2l + 2w = P
[/LIST]
Plugging in our l and P values, we get:
2(6) + 2w = 20
Multiplying through and simplifying, we get:
12 + 2w = 20
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=12%2B2w%3D20&pl=Solve']type this equation into our search engine [/URL]and we get:
w = [B]4[/B]
The perimeter of a rectangular bakery is 204 feet. It is 66 feet long. How wide is it?The perimeter of a rectangular bakery is 204 feet. It is 66 feet long. How wide is it?
Set up the perimeter equation:
2l + 2w = P
Given P = 204 and l = 66, we have:
2(66) + 2w = 204
2w + 132 = 204
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2w%2B132%3D204&pl=Solve']equation solver,[/URL] we get w = [B]36[/B].
The perimeter of a rectangular field is 220 yd. the length is 30 yd longer than the width. Find theThe perimeter of a rectangular field is 220 yd. the length is 30 yd longer than the width. Find the dimensions
We are given the following equations:
[LIST=1]
[*]220 = 2l + 2w
[*]l = w + 30
[/LIST]
Plug (1) into (2)
2(w + 30) + 2w = 220
2w + 60 + 2w = 220
Combine like terms:
4w + 60 = 220
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B60%3D220&pl=Solve']Plug 4w + 60 = 220 into the search engine[/URL], and we get [B]w = 40[/B].
Now plug w = 40 into equation (2)
l = 40 + 30
[B]l = 70[/B]
The perimeter of a rectangular field is 300m. If the width of the field is 59m, what is it’s lengthThe perimeter of a rectangular field is 300m. If the width of the field is 59m, what is it’s length?
Set up the perimeter (P) of a rectangle equation given length (l) and width (w):
2l + 2w = P
We're given P = 300 and w = 59. Plug these into the perimeter equation:
2l + 2(59) = 300
2l + 118 = 300
[URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B118%3D300&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]l = 91[/B]
The perimeter of a rectangular notecard is 16 inches. The notecard is 5 inches wide. How tall is it?The perimeter of a rectangular notecard is 16 inches. The notecard is 5 inches wide. How tall is it?
Perimeter of a rectangle P is:
P = 2l + 2w
We have:
2l + 2w = 16
We are given w = 5, so we have:
2l + 2(5) = 16
2l + 10 = 16
[URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B10%3D16&pl=Solve']Plugging this into our equation calculator[/URL], we get [B]l = 3[/B].
The perimeter of a rectangular outdoor patio is 54 ft. The length is 3 ft greater than the width. WhThe perimeter of a rectangular outdoor patio is 54 ft. The length is 3 ft greater than the width. What are the dimensions of the patio?
Perimeter of a rectangle is:
P = 2l + 2w
We're given l = w + 3 and P = 54. So plug this into our perimeter formula:
54= 2(w + 3) + 2w
54 = 2w + 6 + 2w
Combine like terms:
4w + 6 = 54
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B6%3D54&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 12[/B]
Plug this into our l = w + 3 formula:
l = 12 + 3
[B]l = 15[/B]
The perimeter of a rectangular parking lot is 258 meters. If the length of the parking lot is 71, whThe perimeter of a rectangular parking lot is 258 meters. If the length of the parking lot is 71, what is its width?
The perimeter for a rectangle (P) is given as:
2l + 2w = P
We're given P = 258 and l = 71. Plug these values in:
2(71) + 2w = 258
142 + 2w = 258
[URL='https://www.mathcelebrity.com/1unk.php?num=142%2B2w%3D258&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 58[/B]
The perimeter of a rectangular shelf is 60 inches. The shelf is 7 inches deep. How wide is it?The perimeter of a rectangular shelf is 60 inches. The shelf is 7 inches deep. How wide is it?
The perimeter for a rectangle is given below:
P = 2l + 2w
We're given l = 7 and P = 60. Plug this into the perimeter formula:
60 = 2(7) + 2w
60 = 14 + 2w
Rewritten, it's 2w + 14 = 60.
[URL='https://www.mathcelebrity.com/1unk.php?num=2w%2B14%3D60&pl=Solve']Typing this equation into our search engine[/URL], we get [B]w = 23[/B].
The Radio City Music Hall is selling tickets to Kayla’s premiere at the Rockettes. On the first dayThe Radio City Music Hall is selling tickets to Kayla’s premiere at the Rockettes. On the first day of ticket sales they sold 3 senior citizen tickets and 9 child tickets for a total of $75. It took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price of each senior citizen ticket and each child ticket?
Let the cost of child tickets be c
Let the cost of senior tickets be s
Since revenue = cost * quantity, we're given two equations:
[LIST=1]
[*]9c + 3s = 75
[*]5c + 8s = 67
[/LIST]
To solve this simultaneous group of equations, we can use 3 methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we use, we get the same answer:
[LIST]
[*][B]c = 7[/B]
[*][B]s = 4[/B]
[/LIST]
The revenue for selling x candles is given by f(x)=12x. The teams profit is $40 less than 80% of theThe revenue for selling x candles is given by f(x)=12x. The teams profit is $40 less than 80% of the revenue of selling x candles. write a function g to model the profit.
Profit = Revenue - Cost
We are given the revenue function f(x) = 12x. We are told the profit is 0.8(Revenue) - 40. Our profit function P(x) is:
P(x) = 0.8(12x) - 40
Simplifying, we have:
[B]P(x) = 9.6x - 40[/B]
The school is selling potted plants as a fundraiser. Kara sold 12 ferns and 8 ivy plants for 260.00.The school is selling potted plants as a fundraiser. Kara sold 12 ferns and 8 ivy plants for 260.00. Paul sold 15 ivy plants and 6 ferns for 240. What’s the selling price of each plant.
Let the cost of each fern be f
Let the cost of each ivy plant be I
We're given:
[LIST=1]
[*]12f + 8i = 260
[*]15i + 6f = 240
[/LIST]
To solve this system of equations, we can use 3 methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12f+%2B+8i+%3D+260&term2=15f+%2B+6i+%3D+240&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12f+%2B+8i+%3D+260&term2=15f+%2B+6i+%3D+240&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12f+%2B+8i+%3D+260&term2=15f+%2B+6i+%3D+240&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
[LIST]
[*][B]f = 7.5[/B]
[*][B]i= 21.25[/B]
[/LIST]
The senior class at high school A and high school B planned separate trips to the state fair. ThereThe senior class at high school A and high school B planned separate trips to the state fair. There senior class and high school A rented and filled 10 vans and 6 buses with 276 students. High school B rented and filled 5 vans and 2 buses with 117 students. Every van had the same number of students in them as did the buses. How many students can a van carry?? How many students can a bus carry??
Let b be the number of students a bus can carry. Let v be the number of students a van can carry. We're given:
[LIST=1]
[*]High School A: 10v + 6b = 276
[*]High School B: 5v + 2b = 117
[/LIST]
We have a system of equations. We can solve this 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10v+%2B+6b+%3D+276&term2=5v+%2B+2b+%3D+117&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10v+%2B+6b+%3D+276&term2=5v+%2B+2b+%3D+117&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10v+%2B+6b+%3D+276&term2=5v+%2B+2b+%3D+117&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get:
[LIST]
[*][B]b = 21[/B]
[*][B]v = 15[/B]
[/LIST]
The sum of 2 consecutive numbers is 3 less than 3 times the first number. What are the numbers?The sum of 2 consecutive numbers is 3 less than 3 times the first number. What are the numbers?
Let the first number be x. And the second number be y. We're given:
[LIST=1]
[*]y = x + 1
[*]x + y = 3x - 3 (less 3 means subtract 3)
[/LIST]
Substitute (1) into (2):
x + x + 1 = 3x - 3
Combine like terms:
2x + 1 = 3x - 3
[URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B1%3D3x-3&pl=Solve']Type this equation into the search engine[/URL], we get:
x = 4
Substituting x = 4 into equation 1:
y = 4 + 1
y = 5
So (x, y) = [B](4, 5)[/B]
the sum of 2 numbers is 5. 5 times the larger number plus 4 times the smaller number is 37. Find thethe sum of 2 numbers is 5. 5 times the larger number plus 4 times the smaller number is 37. Find the numbers
Let the first small number be x. Let the second larger number be y. We're given:
[LIST=1]
[*]x + y = 5
[*]5y + 4x = 37
[/LIST]
We can solve this 3 ways, using the following methods:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y%3D5&term2=5y+%2B+4x+%3D+37&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y%3D5&term2=5y+%2B+4x+%3D+37&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y%3D5&term2=5y+%2B+4x+%3D+37&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we choose, we get:
[B]x = -12
y = 17
[/B]
Let's check our work using equation 1:
-12 + 17 ? 5
5 = 5 <-- Check
Let's check our work using equation 2:
5(17) + 4(-12) ? 37
85 - 48 ? 37
37 = 37 <-- Check
The sum of 2 numbers is 60. The larger number is thrice the smallerThe sum of 2 numbers is 60. The larger number is thrice the smaller.
Let the 2 numbers be x and y, where x is the smaller number and y is the larger number. We are given:
[LIST=1]
[*]x + y = 60
[*]y = 3x
[/LIST]
Substitute (2) into (1):
x + (3x) = 60
Combine like terms:
4x = 60
[URL='https://www.mathcelebrity.com/1unk.php?num=4x%3D60&pl=Solve']Type 4x = 60 into our search engine[/URL], and you get [B]x = 15[/B].
Substituting x = 15 into Equation (2) above, we get:
y = 3(15)
[B]y = 45
[/B]
Check our work in Equation (1):
15 + 45 ? 60
60 = 60
Check our work in Equation (2):
45 ? 15(3)
45 = 45
The numbers check out, so our answer is [B](x, y) = (15, 45)[/B]
The sum of 3, 7, and a number amounts to 16The sum of 3, 7, and a number amounts to 16
Let the number be n. A sum means we add. We're given:
3 + 7 + n = 16
Grouping like terms, we get:
n + 10 = 16
[URL='https://www.mathcelebrity.com/1unk.php?num=n%2B10%3D16&pl=Solve']Typing this equation into our search engine[/URL], we get:
n = [B]6 [/B]
The sum of Jocelyn and Joseph's age is 40. In 5 years, Joseph will be twice as Jocelyn's present ageThe sum of Jocelyn and Joseph's age is 40. In 5 years, Joseph will be twice as Jocelyn's present age. How old are they now?
Let Jocelyn's age be a
Let Joseph's age be b.
We're given two equations:
[LIST=1]
[*]a + b = 40
[*]2(a + 5) = b + 5
[/LIST]
We rearrange equation (1) in terms of a to get:
[LIST=1]
[*]a = 40 - b
[*]2a = b + 5
[/LIST]
Substitute equation (1) into equation (2) for a:
2(40 - b) = b + 5
80 - 2b = b + 5
To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=80-2b%3Db%2B5&pl=Solve']type it in our search engine[/URL] and we get:
[B]b (Joseph's age) = 25[/B]
Now, substitute b = 25 into equation (1) to solve for a:
a = 40 - 25
[B]a (Jocelyn's age) = 15[/B]
The sum of Mr. Adams and Mrs. Benson's age is 55. The difference is 3. What are their ages?The sum of Mr. Adams and Mrs. Benson's age is 55. The difference is 3. What are their ages?
[U]Givens[/U]
[LIST]
[*]Let Mr. Adam's age be a
[*]Let Mrs. Benson's age be b
[*]We're given two equations where [I]sum[/I] means we add and [I]difference[/I] means we subtract:
[/LIST]
[LIST=1]
[*]a + b = 55
[*]a - b = 3
[/LIST]
Since we have opposite coefficients for b, we can take a shortcut and add equation 1 to equation 2:
(a + a) + (b - b) = 55 + 3
Combining like terms and simplifying, we get:
2a = 58
To solve this equation for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=2a%3D58&pl=Solve']type it in our search engine[/URL] and we get:
a = [B]29
[/B]
If a = 29, then we plug this into equation (1) to get:
29 + b = 55
b = 55 - 29
b = [B]26
[MEDIA=youtube]WwkpNqPvHs8[/MEDIA][/B]
The sum of the ages of levi and renee is 89 years. 7 years ago levi's age was 4 times renees age. HoThe sum of the ages of levi and renee is 89 years. 7 years ago levi's age was 4 times renees age. How old is Levi now?
Let Levi's current age be l. Let Renee's current age be r. Were given two equations:
[LIST=1]
[*]l + r = 89
[*]l - 7 = 4(r - 7)
[/LIST]
Simplify equation 2 by multiplying through:
[LIST=1]
[*]l + r = 89
[*]l - 7 = 4r - 28
[/LIST]
Rearrange equation 1 to solve for r and isolate l by subtracting l from each side:
[LIST=1]
[*]r = 89 - l
[*]l - 7 = 4r - 28
[/LIST]
Now substitute equation (1) into equation (2):
l - 7 = 4(89 - l) - 28
l - 7 = 356 - 4l - 28
l - 7 = 328 - 4l
To solve for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=l-7%3D328-4l&pl=Solve']type the equation into our search engine[/URL] and we get:
l = [B]67[/B]
The sum of the digits of a 2 digit number is 10. The value of the number is four more than 15 timesThe sum of the digits of a 2 digit number is 10. The value of the number is four more than 15 times the unit digit. Find the number.
Let the digits be (x)(y) where t is the tens digit, and o is the ones digit. We're given:
[LIST=1]
[*]x + y = 10
[*]10x+ y = 15y + 4
[/LIST]
Simplifying Equation (2) by subtracting y from each side, we get:
10x = 14y + 4
Rearranging equation (1), we get:
x = 10 - y
Substitute this into simplified equation (2):
10(10 - y) = 14y + 4
100 - 10y = 14y + 4
[URL='https://www.mathcelebrity.com/1unk.php?num=100-10y%3D14y%2B4&pl=Solve']Typing this equation into our search engine[/URL], we get:
y = 4
Plug this into rearranged equation (1), we get:
x = 10 - 4
x = 6
So our number xy is [B]64[/B].
Let's check our work against equation (1):
6 + 4 ? 10
10 = 10
Let's check our work against equation (2):
10(6)+ 4 ? 15(4) + 4
60 + 4 ? 60 + 4
64 = 64
The sum of two numbers is 231. The larger is twice the smaller. What are the numbers?Let x be the larger number.
Let y be the smaller number.
We're given two equations:
[LIST=1]
[*]x + y = 231
[*]x = 2y
[/LIST]
Substitute (2) into (1) for x:
2y + y = 231
3y = 231
[URL='https://www.mathcelebrity.com/1unk.php?num=3y%3D231&pl=Solve']Type this into our math solver[/URL] and get
y = 77
This means x is:
x = 2(77)
x = [B]154[/B]
The team A scored 13 more points than Team B. The total of their score was 47. How many points did tThe team A scored 13 more points than Team B. The total of their score was 47. How many points did team A score?
Let a be the amount of points A scored, and b be the amount of points B scored. We're given:
[LIST=1]
[*]a = b + 13
[*]a + b = 47
[/LIST]
Plug (1) into (2)
(b + 13) + b = 47
Combine like terms:
2b + 13 = 47
[URL='https://www.mathcelebrity.com/1unk.php?num=2b%2B13%3D47&pl=Solve']Typing this equation into our search engine[/URL], we get:
b = 17
Now plug this into (1):
a = 17 + 13
a = [B]30[/B]
The total age of three cousins is 48. Suresh is half as old as Hakima and 4 years older than Saad. hThe total age of three cousins is 48. Suresh is half as old as Hakima and 4 years older than Saad. How old are the cousins?
Let a be Suresh's age, h be Hakima's age, and c be Saad's age. We're given:
[LIST=1]
[*]a + h + c = 48
[*]a = 0.5h
[*]a = c + 4
[/LIST]
To isolate equations in terms of Suresh's age (a), let's do the following:
[LIST]
[*]Rewriting (3) by subtracting 4 from each side, we get c = a - 4
[*]Rewriting (2) by multiply each side by 2, we have h = 2a
[/LIST]
We have a new system of equations:
[LIST=1]
[*]a + h + c = 48
[*]h = 2a
[*]c = a - 4
[/LIST]
Plug (2) and (3) into (1)
a + (2a) + (a - 4) = 48
Group like terms:
(1 + 2 + 1)a - 4 = 48
4a - 4 = 48
[URL='https://www.mathcelebrity.com/1unk.php?num=4a-4%3D48&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]a = 13 [/B]<-- Suresh's age
This means that Hakima's age, from modified equation (2) above is:
h = 2(13)
[B]h = 26[/B] <-- Hakima's age
This means that Saad's age, from modified equation (3) above is:
c = 13 - 4
[B]c = 9[/B] <-- Saad's age
[B]
[/B]
The total cost for 9 bracelets, including shipping was $72. The shipping charge was $9. Define yourThe total cost for 9 bracelets, including shipping was $72. The shipping charge was $9. Define your variable and write an equation that models the cost of each bracelet.
We set up a cost function as fixed cost plus total cost. Fixed cost is the shipping charge of $9. So we have the following cost function where n is the cost of the bracelets:
C(b) = nb + 9
We are given C(9) = 72 and b = 9
9n + 9 = 72
[URL='https://www.mathcelebrity.com/1unk.php?num=9n%2B9%3D72&pl=Solve']Run this through our equation calculator[/URL], and we get [B]n = 7[/B].
The value of all the quarters and dimes in a parking meter is $18. There are twice as many quartersThe value of all the quarters and dimes in a parking meter is $18. There are twice as many quarters as dimes. What is the total number of dimes in the parking meter?
Let q be the number of quarters. Let d be the number of dimes. We're given:
[LIST=1]
[*]q = 2d
[*]0.10d + 0.25q = 18
[/LIST]
Substitute (1) into (2):
0.10d + 0.25(2d) = 18
0.10d + 0.5d = 18
[URL='https://www.mathcelebrity.com/1unk.php?num=0.10d%2B0.5d%3D18&pl=Solve']Type this equation into our search engine[/URL], and we get [B]d = 30[/B].
The width of a rectangle is fixed at 4cm. For what lengths will the area be less than 86 cm^2The width of a rectangle is fixed at 4cm. For what lengths will the area be less than 86 cm^2
The Area (A) of a rectangle is given by:
A = lw
With an area of [I]less than[/I] 86 and a width of 4, we have the following inequality:
4l < 86
To solve for l, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=4l%3C86&pl=Show+Interval+Notation']type this inequality into our search engine[/URL] and we get:
[B]l < 21.5[/B]
there are $4.20 in nickel and quarters. There are 6 more nickels than quarters there. How many coinsthere are $4.20 in nickel and quarters. There are 6 more nickels than quarters there. How many coins of each are there
We're given two equations:
[LIST=1]
[*]n = q + 6
[*]0.05n + 0.25q = 4.2
[/LIST]
Substitute equation (1) into equation (2):
0.05(q + 6) + 0.25q = 4.2
Multiply through and simplify:
0.05q + 0.3 + 0.25q
0.3q + 0.3 = 4.2
To solve for q, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.3q%2B0.3%3D4.2&pl=Solve']type this equation into the search engine[/URL] and we get:
q = [B]13
[/B]
To solve for n, we plug in q = 13 into equation (1):
n = 13 + 6
n = [B]19[/B]
There are 1000 juniors in a college. Among the 1000 juniors, 200 students are taking STAT200, and 10There are 1000 juniors in a college. Among the 1000 juniors, 200 students are taking STAT200, and 100 students are taking PSYC300. There are 50 students taking both courses.
a) What is the probability that a randomly selected junior is taking at least one of these two courses?
b) What is the probability that a randomly selected junior is taking PSYC300, given that he/she is taking STAT200?
a) P(A U B) = P(A) + P(B) - P(A ? B) = 0.2 + 0.1 - 0.05 = [B]0.25[/B]
b) P(SYC|STAT) = P(STAT ? SYC)/P(STAT) = 0.05/0.2 = [B]0.25[/B]
There are 13 animals in the barn. some are chickens and some are pigs. there are 40 legs in all. HowThere are 13 animals in the barn. some are chickens and some are pigs. there are 40 legs in all. How many of each animal are there?
Chickens have 2 legs, pigs have 4 legs. Let c be the number of chickens and p be the number of pigs. Set up our givens:
(1) c + p = 13
(2) 2c + 4p = 40
[U]Rearrange (1) to solve for c by subtracting p from both sides:[/U]
(3) c = 13 - p
[U]Substitute (3) into (2)[/U]
2(13 - p) + 4p = 40
26 - 2p + 4p = 40
[U]Combine p terms[/U]
2p + 26 = 40
[U]Subtract 26 from each side:[/U]
2p = 14
[U]Divide each side by 2[/U]
[B]p = 7[/B]
[U]Substitute p = 7 into (3)[/U]
c = 13 - 7
[B]c = 6[/B]
For a shortcut, you could use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+p+%3D+13&term2=2c+%2B+4p+%3D+40&pl=Cramers+Method']simultaneous equations calculator[/URL]
There are 2 consecutive integers. Twice the first increased by the second yields 16. What are the nuThere are 2 consecutive integers. Twice the first increased by the second yields 16. What are the numbers?
Let x be the first integer. y = x + 1 is the next integer. We have the following givens:
[LIST=1]
[*]2x + y = 16
[*]y = x + 1
[/LIST]
Substitute (2) into (1)
2x + (x + 1) = 16
Combine x terms
3x + 1 = 16
Subtract 1 from each side
3x = 15
Divide each side by 3
[B]x = 5[/B]
So the other integer is 5 + 1 = [B]6[/B]
There are 33 students in an Algebra I class. There are 7 fewer girls than boys. How many girls are iThere are 33 students in an Algebra I class. There are 7 fewer girls than boys. How many girls are in the class?
Let b be the number of boys and g be the number of girls. We are given 2 equations:
[LIST=1]
[*]g = b - 7
[*]b + g = 33
[/LIST]
Substitute (1) into (2):
b + (b - 7) = 33
Combine like terms:
2b - 7 = 33
[URL='https://www.mathcelebrity.com/1unk.php?num=2b-7%3D33&pl=Solve']Typing this equation into our search engine[/URL], we get b = 20.
Since the problem asks for how many girls (g) we have, we substitute b = 20 into Equation (1):
g = 20 - 7
[B]g = 13[/B]
There are 812 students in a school. There are 36 more girls than boys. How many girls are there?[SIZE=6]There are 812 students in a school. There are 36 more girls than boys. How many girls are there?
Let b be boys
Let g be girls
We're given two equations:[/SIZE]
[LIST=1]
[*][SIZE=6]b + g = 812[/SIZE]
[*][SIZE=6]g = b + 36[/SIZE]
[/LIST]
[SIZE=6]Rearrange equation 2 to subtract b from each side:
[/SIZE]
[LIST=1]
[SIZE=6]
[LIST][*]b + g = 812[/LIST]
[LIST][*]-b + g = 36[/LIST][/SIZE]
[/LIST]
[SIZE=6]Add equation (1) to equation (2):
b - b + 2g = 812 + 36
The b's cancel:
2g = 848
Divide each side by 2:
2g/2 = 848/2
g = [B]424[/B]
[B][/B]
To find b, we put g= 424 into equation 1:
b + 424 = 812
b = 812 - 424
b = [B]388[/B]
[MEDIA=youtube]JO1b7qVwWoI[/MEDIA]
[/SIZE]
There is a stack of 10 cards, each given a different number from 1 to 10. suppose we select a card rThere is a stack of 10 cards, each given a different number from 1 to 10. Suppose we select a card randomly from the stack, replace it, and then randomly select another card. What is the probability that the first card is an odd number and the second card is greater than 7.
First Event: P(1, 3, 5, 7, 9) = 5/10 = 1/2 or 0.5
Second Event: P(8, 9, 10) = 3/10 or 0.3
Probability of both events since each is independent is 1/2 * 3/10 = 3/20 = [B]0.15 or 15%[/B]
There were 175 tickets sold for the upcoming event in the gym. If students tickets cost $5 and adultThere were 175 tickets sold for the upcoming event in the gym. If students tickets cost $5 and adult tickets are $8, tell me how many tickets were sold if gate receipts totaled $1028?
Let s be the number of student tickets and a be the number of adult tickets. We are given:
a + s = 175
8a + 5s = 1028
There are 3 ways to solve this, all of which give us:
[B]a = 51
s = 124
[/B]
[URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+175&term2=8a+%2B+5s+%3D+1028&pl=Substitution']Substitution Method[/URL]
[URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+175&term2=8a+%2B+5s+%3D+1028&pl=Elimination']Elimination Method[/URL]
[URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+175&term2=8a+%2B+5s+%3D+1028&pl=Cramers+Method']Cramers Method[/URL]
Thin Lens DistanceFree Thin Lens Distance Calculator - Given two out of three items in the thin lens equation, this solves for the third.
Three people went to lunch and bought a large meal which they all split. The total cost, including tThree people went to lunch and bought a large meal which they all split. The total cost, including tip, was $30. Each person paid $10 to the waitress and started to leave the restaurant. As they left, the waitress came running up to them with five dollars saying that she made a mistake and that the meal and tip should have cost only $25.
The waitress then gave each person one dollar, but didn't know how to split the remaining two dollars. They told her to keep the extra two dollars as an additional tip.
When the people started talking about what had just happened, they started getting confused. They had each paid $10 for the meal and received one dollar back, so they each really paid $9 for the meal for a total of $27. Add the two dollars of extra tip and the total is $29. Where did the extra one dollar go?
[B]The missing dollar is not really missing. The cost of the meal is really $27. The $25 plus the extra two dollar tip was given to the waitress -- $27
What we have is the cost ($27) plus the refund ($3) = $30.
The $30 that was originally paid is accounted for as follows:
Restaurant + regular waitress tip: $25
Three people: $3 (refund)
Waitress: $2 (extra tip)
$25 + $3 + $2 = $30[/B]
Tina's mom made brownies. When tinas friend came over they ate 1/3 of the brownies. Her sister ate 2Tina's mom made brownies. When tinas friend came over they ate 1/3 of the brownies. Her sister ate 2 and her dad ate 4. If there are 26 brownies left. How many did her mom make
Let b denote the number of brownies Tina's mom made. We're given:
b - 1/3b - 2 - 4 = 26
Combining like terms, we have:
2b/3 - 6 = 26
Add 6 to each side, we get:
2b/3 = 32
To solve this equation for b, we [URL='https://www.mathcelebrity.com/prop.php?num1=2b&num2=32&den1=3&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our math engine[/URL] and we get:
b = [B]48[/B]
To be a member of world fitness gym, it costs $60 flat fee and $30 per month. Maria has paid a totalTo be a member of world fitness gym, it costs $60 flat fee and $30 per month. Maria has paid a total of $210 for her gym membership so far. How long has Maria been a member to the gym?
The cost function C(m) where m is the number of months for the gym membership is:
C(m) = 30m + 60
We're given that C(m) = 210 for Maria. We want to know the number of months (m) that Maria has been a member.
With C(m) = 210, we have:
30m + 60 =210
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=30m%2B60%3D210&pl=Solve']we type it in our search engine[/URL] and we get:
m = [B]5[/B]
To convert from Celsius to Fahrenheit, multiply by 1.8 and add 32. Write a formula to describe thisTo convert from Celsius to Fahrenheit, multiply by 1.8 and add 32. Write a formula to describe this relationship.
Given C as Celsius and F as Fahrenheit, we have the following equation:
[B]F = 1.8C + 32[/B]
To rent a building for a school dance, Ava paid 120 plus 2.50 for each student. To attend the schoolTo rent a building for a school dance, Ava paid 120 plus 2.50 for each student. To attend the school all together Ava paid 325. How many students attended the dance?
Let the number of students be s. We're given
2.50s + 120 = 325
[URL='https://www.mathcelebrity.com/1unk.php?num=2.50s%2B120%3D325&pl=Solve']Type this equation into our search engine[/URL], and we get:
s = [B]82[/B]
To rent a car it costs $12 per day and $0.50 per kilometer traveled. If a car were rented for 5 daysTo rent a car it costs $12 per day and $0.50 per kilometer traveled. If a car were rented for 5 days and the charge was $110.00, how many kilometers was the car driven?
Using days as d and kilometers as k, we have our cost equation:
Rental Charge = $12d + 0.5k
We're given Rental Charge = 110 and d = 5, so we plug this in:
110 = 12(5) + 0.5k
110 = 60 + 0.5k
[URL='https://www.mathcelebrity.com/1unk.php?num=60%2B0.5k%3D110&pl=Solve']Plugging this into our equation calculator[/URL], we get:
[B]k = 100[/B]
Today is my birthday! Four-fifths of my current age is greater than three-quarters of my age one yeaToday is my birthday! Four-fifths of my current age is greater than three-quarters of my age one year from now. Given that my age is an integer number of years, what is the smallest my age could be?
Let my current age be a. We're given:
4/5a > 3/4(a + 1)
Multiply through on the right side:
4a/5 > 3a/4 + 3/4
Let's remove fractions by multiply through by 5:
5(4a/5) > 5(3a/4) + 5(3/4)
4a > 15a/4 + 15/4
Now let's remove the other fractions by multiply through by 4:
4(4a) > 4(15a/4) + 4(15/4)
16a > 15a + 15
[URL='https://www.mathcelebrity.com/1unk.php?num=16a%3E15a%2B15&pl=Solve']Typing this inequality into our search engine[/URL], we get:
a > 15
This means the smallest [I]integer age[/I] which the problem asks for is:
15 + 1 = [B]16[/B]
Tomás is a salesperson who earns a monthly salary of $2250 plus a 3% commission on the total amountTomás is a salesperson who earns a monthly salary of $2250 plus a 3% commission on the total amount of his sales. What were his sales last month if he earned a total of $4500?
Let total sales be s. We're given the following earnings equation:
0.03s + 2250 = 4500
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.03s%2B2250%3D4500&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]75,000[/B]
TorusFree Torus Calculator - Calculates the volume of a torus and surface area of a torus given major radius and minor radius.
Total RevenueFree Total Revenue Calculator - Given a quantity, price, and item, this calculates the total revenue.
TrapezoidsFree Trapezoids Calculator - This calculator determines the following items for a trapezoid based on given inputs:
* Area of trapezoid
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triangle sum theoremThe triangle sum theorem states the sum of the three angles in a triangle equals 180 degrees.
So if you're given two angles and need too find the 3rd angle, add the 2 known angles up, and subtract them from 180 to get the 3rd angle measure.
Trig MeasurementFree Trig Measurement Calculator - Given an angle θ, this calculates the following measurements:
Sin(θ) = Sine
Cos(θ) = Cosine
Tan(θ) = Tangent
Csc(θ) = Cosecant
Sec(θ) = Secant
Cot(θ) = Cotangent
Arcsin(x) = θ = Arcsine
Arccos(x) = θ = Arccosine
Arctan(x) =θ = Arctangent
Also converts between Degrees and Radians and Gradians
Coterminal Angles as well as determine if it is acute, obtuse, or right angle. For acute angles, a cofunction will be determined. Also shows the trigonometry function unit circle
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Twice a first number decreased by a second number is 16. The first number increased by 3 times the sTwice a first number decreased by a second number is 16. The first number increased by 3 times the second number is 1. Find the numbers.
Let the first number be x and the second number be y. We're given:
[LIST=1]
[*]2x - y = 16
[*]x + 3y = 1
[/LIST]
Using our simultaneous equations calculator, you can solve this 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+y+%3D+16&term2=x+%2B+3y+%3D+1&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+y+%3D+16&term2=x+%2B+3y+%3D+1&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+y+%3D+16&term2=x+%2B+3y+%3D+1&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
No matter what method we use, we get the same answers:
[B]x = 7
y = -2
(x, y) = (7, -2)
[/B]
Let's check our work in equation 1:
2(7) - -2 ? 16
14 + 2 ? 16
16 = 16 <-- Check
Let's check our work in equation 2:
7 + 3(-2) ? 1
7 - 6 ? 1
1 = 1 <-- Check
two numbers have an average of 2100 and one number is $425 more than the other number. What are thetwo numbers have an average of 2100 and one number is $425 more than the other number. What are the numbers
Let the first number be x and the second number be y. We're given two equations:
[LIST=1]
[*](x + y)/2 = 2100 (Average)
[*]y = x + 425
[/LIST]
Rearrange equation (1) by cross multiplying
x + y = 2 * 2100
x + y = 4200
So we have our revised set of equations:
[LIST=1]
[*]x + y = 4200
[*]y = x + 425
[/LIST]
Substituting equation (2) into equation (1) for y, we get:
x + (x + 425) = 4200
Combining like terms, we get:
2x + 425 = 4200
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B425%3D4200&pl=Solve']equation solver[/URL], we get:
x = [B]1887.5[/B]
Which means using equation (2), we get
y = 1887.5 + 425
y = [B]2312.5[/B]
Two numbers that total 44 and have a difference of 6Two numbers that total 44 and have a difference of 6.
Let the two numbers be x and y. We're given the following equations:
[LIST=1]
[*]x + y = 44 <-- Total means a sum
[*]x - y = 6
[/LIST]
Add the two equations together:
(x + x) + (y - y) = 44 + 6
Cancelling the y terms, we have:
2x = 50
[URL='https://www.mathcelebrity.com/1unk.php?num=2x%3D50&pl=Solve']Typing this equation into the search engine[/URL], we get:
[B]x = 25
[/B]
Rearranging equation (2) above, we get:
y = x - 6
Substituting x = 25 into this, we get:
y = 25 - 6
[B]y = 19[/B]
Two numbers total 12, and their differences is 20. Find the two numbers.Two numbers total 12, and their differences is 20. Find the two numbers.
Let the first number be x. Let the second number be y. We're given two equations:
[LIST=1]
[*]x + y = 12
[*]x - y = 20
[/LIST]
Since we have y coefficients of (-1 and 1) that cancel, we add the two equations together:
(x + x) + (y - y) = 12 + 20
The y terms cancel, so we have:
2x = 32
[URL='https://www.mathcelebrity.com/1unk.php?num=2x%3D32&pl=Solve']Type this equation into our search engine[/URL] and we get:
x = [B]16[/B]
Substitute this value of x = 16 back into equation 1:
16 + y = 12
[URL='https://www.mathcelebrity.com/1unk.php?num=16%2By%3D12&pl=Solve']Typing this equation into our search engine[/URL], we get:
y = [B]-4
[/B]
Now, let's check our work for both equations:
[LIST=1]
[*]16 - 4 = 12
[*]16 - -4 --> 16 + 4 = 20
[/LIST]
So these both check out.
(x, y) = ([B]16, -4)[/B]
Two numbers total 83 and have a difference of 17 find the two numbersLet the numbers be x and y. Set up our givens:
[LIST=1]
[*]x + y = 83
[*]x - y = 17
[/LIST]
[U]Add equation (1) to equation (2)[/U]
x + x + y - y = 83 + 17
[U]The y-terms cancel out:[/U]
2x = 100
[U]Divide each side by 2:[/U]
2x/2= 100/2
x = [B]50[/B]
[U]
Plug x = 50 into equation (1)[/U]
50 + y = 83
[U]Subtract 50 from each side:[/U]
50 - 50 + y = 83 - 50
[U]Cancel the 50 on the left side:[/U]
y = [B]33
[/B]
So our two numbers (x, y) = (33, 50)
[MEDIA=youtube]jajO043ChUM[/MEDIA]
Tyrone re sells 3 pairs of Yeezys and a pair of Nikes for 250$. Nucci re sells a pair of Yeezys andTyrone re sells 3 pairs of Yeezys and a pair of Nikes for 250$. Nucci re sells a pair of Yeezys and Nikes for 150$ How much does a pair of Yeezys cost?
Let y be the cost of Yeezy's and n be the cost of Nike's. We're given two equations:
[LIST=1]
[*]3y + n = 250
[*]y + n = 150
[/LIST]
We have a system of equations, and we can solve it using one of three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3y+%2B+n+%3D+250&term2=y+%2B+n+%3D+150&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3y+%2B+n+%3D+250&term2=y+%2B+n+%3D+150&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3y+%2B+n+%3D+250&term2=y+%2B+n+%3D+150&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we choose, we get:
[LIST]
[*][B]n = 100[/B]
[*][B]y = 50[/B]
[/LIST]
Units of Output (Service Output) DepreciationFree Units of Output (Service Output) Depreciation Calculator - Given an asset value, salvage value, production units, and units per period, this calculates the depreciation per period using the units of output depreciation (service output depreciation)
Utility and Cost Utility RatioFree Utility and Cost Utility Ratio Calculator - Given 2 methods with a set of utilities and weights/probabilities, this will calculate the utility for each method, as well as the total utility using the additive method, as well as the Cost Utility Ratio
Van needs to enter a formula into a spreadsheet to show the outputs of an arithmetic sequence that sVan needs to enter a formula into a spreadsheet to show the outputs of an arithmetic sequence that starts with 13 and continues to add seven to each output. For now, van needs to know what the 15th output will be. Complete the steps needed to determine the 15th term in sequence.
Given a first term a1 of 13 and a change amount of 7, expand the series
The explicit formula for an [I]arithmetic series[/I] is an = a1 + (n - 1)d
d represents the common difference between each term, an - an - 1
Looking at all the terms, we see the common difference is 7, and we have a1 = 13
Therefore, our explicit formula is an = 13 + 7(n - 1)
If n = 15, then we plug it into our explicit formula above:
an = 13 + 7(n - 1)
a(15) = 15 + 7(15 - 1)
a(15) = 15 + 7 * 14
a(15) = 15 + 98
a(15) = [B]113[/B]
VectorsFree Vectors Calculator - Given 2 vectors A and B, this calculates:
* Length (magnitude) of A = ||A||
* Length (magnitude) of B = ||B||
* Sum of A and B = A + B (addition)
* Difference of A and B = A - B (subtraction)
* Dot Product of vectors A and B = A x B
A ÷ B (division)
* Distance between A and B = AB
* Angle between A and B = θ
* Unit Vector U of A.
* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).
* Cauchy-Schwarz Inequality
* The orthogonal projection of A on to B, projBA and and the vector component of A orthogonal to B → A - projBA
Also calculates the horizontal component and vertical component of a 2-D vector.
Venn Diagram (2 circles)Free Venn Diagram (2 circles) Calculator - Given two circles A and B with an intersection piece of C, this will calculate all relevant probabilities of the Venn Diagram.
Verbal PhraseFree Verbal Phrase Calculator - Given an algebraic expression, this translates back to a verbal phrase
Victoria is 4 years older than her neighbor. The sum of their ages is no more than 14 years.Victoria is 4 years older than her neighbor. The sum of their ages is no more than 14 years.
Let Victoria's age be v. And her neighbor's age be n. We're given:
[LIST=1]
[*]v = n + 4
[*]v + n <=14 <-- no more than means less than or equal to
[/LIST]
Substitute Equation (1) into Inequality (2):
(n + 4) + n <= 14
Combine like terms:
2n + 4 <= 14
[URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B4%3C%3D14&pl=Solve']Typing this inequality into our search engine[/URL], we get:
n <= 5
Substituting this into inequality (2):
v + 5 <= 14
[URL='https://www.mathcelebrity.com/1unk.php?num=v%2B5%3C%3D14&pl=Solve']Typing this inequality into our search engine[/URL], we get:
[B]v <= 9[/B]
VolatilityFree Volatility Calculator - Given a set of stock prices, this determines expected rates of return and volatility
Walking Distance (Pedometer)Free Walking Distance (Pedometer) Calculator - Given a number of steps and a distance per stride in feet, this calculator will determine how far you walk in other linear measurements.
Warren was making $100,000 per year. His boss said that he was going to cut his salary 25%, but thatWarren was making $100,000 per year. His boss said that he was going to cut his salary 25%, but that Warren shouldn't worry because he would be given a 25% raise the next day. How much will Warren's salary be after the 25% cut and 25% raise?
Cut salary:
100,000 * 0.75 = 75,000
New salary after raise:
75,000 * 1.25 = [B]93,750[/B]
Weighted Average Cost of Capital (WACC) and Capital Asset Pricing Model (CAPM)Free Weighted Average Cost of Capital (WACC) and Capital Asset Pricing Model (CAPM) Calculator - Calculates the Weighted Average Cost of Capital (WACC) and also calculates the return on equity if not given using the Capital Asset Pricing Model (CAPM) using debt and other inputs such as Beta and risk free rate.
what integer is tripled when 9 is added to 3 fourths of it?what integer is tripled when 9 is added to 3 fourths of it?
Let the integer be n. Tripling an integer means multiplying it by 3. We're given:
3n = 3n/4 + 9
Since 3 = 12/4, we have:
12n/4 = 3n/4 + 9
Subtract 3n/4 from each side:
9n/4 = 9
[URL='https://www.mathcelebrity.com/prop.php?num1=9n&num2=9&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this equation into the search engine[/URL], we get:
[B]n = 4[/B]
What is the formula for the area of a circle?What is the formula for the area of a circle?
Given a radius r, we have Area (A) of:
[B]A = ?r^2[/B]
What is the formula for the circumference of a circle?What is the formula for the circumference of a circle?
Given radius r and diameter d, the circumference C is:
[B]C = 2?r or ?d[/B]
Which of the following equations represents a line that is parallel to the line with equation y = -3Which of the following equations represents a line that is parallel to the line with equation y = -3x + 4?
A) 6x + 2y = 15
B) 3x - y = 7
C) 2x - 3y = 6
D) x + 3y = 1
Parallel lines have the same slope, so we're looking for a line with a slope of 3, in the form y = mx + b. For this case, we want a line with a slope of -3, like our given line.
If we rearrange A) by subtracting 6x from each side, we get:
2y = -6x + 15
Divide each side by 2, we get:
y = -3x + 15/2
This line is in the form y = mx + b, where m = -3. So our answer is [B]A[/B].
Wilbie had candy to give to his 3 children. He first took 5 pieces and evenly divided the rest amongWilbie had candy to give to his 3 children. He first took 5 pieces and evenly divided the rest among each child. Each child received 3 pieces. With how many pieces did he start?
Let the starting candy amount be c. We're given:
(c - 5)/3 = 3
Cross multiply:
c - 5 = 3*3
c - 5 = 9
[URL='https://www.mathcelebrity.com/1unk.php?num=c-5%3D9&pl=Solve']Type this equation into the search engine[/URL], and we get:
c = 14
Wind Chill FactorFree Wind Chill Factor Calculator - This calculator determines the wind chill factor given a temperature in F° and a wind speed in miles per hour (mph). Simply enter your temperature and wind speed and press the button
Work Word ProblemsFree Work Word Problems Calculator - Given Person or Object A doing a job in (r) units of time and Person or Object B doing a job in (s) units of time, this calculates how long it would take if they combined to do the job.
Write an equation in slope-intercept form for the line with slope 4 and y-intercept -7Write an equation in slope-intercept form for the line with slope 4 and y-intercept -7
The standard equation for slope (m) and y-intercept (b) is given as:
y = mx + b
We're given m = 4 and y-intercept = -7, so we have:
[B]y = 4x - 7[/B]
Yolanda is riding her bicycle. She rides for 5 hours at a speed of 12.5 kilometers per hours. For hoYolanda is riding her bicycle. She rides for 5 hours at a speed of 12.5 kilometers per hours. For how many kilometers does she ride?
This is a distance problem, where distance = rate * time. We are given time of 5 hours, at a rate of 12.5km/hour.
Using our [URL='http://www.mathcelebrity.com/drt.php?d=+&r=12.5&t=5&pl=Calculate+the+missing+Item+from+D%3DRT']distance calculator[/URL], we get D = [B]62.5km[/B].
Yosemite National Park charges $7 per person for an all day admission to the park. The total cost foYosemite National Park charges $7 per person for an all day admission to the park. The total cost for n people to go to the park all day is given by the expression 7n. 8 friends go to the park on Saturday. What is the total cost of admission?
We want to evaluate f(n) = 7n for n = 8
f(8) = 7(8) = [B]56[/B]
You are baking muffins for your class. There are 17 total students in your class and you have bakedYou are baking muffins for your class. There are 17 total students in your class and you have baked 5 muffins. Write and solve an equation to find the additional number x of muffins you need to bake in order to have 2 muffins for each student. Write your equation so that the units on each side of the equation are muffins per student.
2 muffins per student = 17*2 = 34 muffins.
We have an equation with a given 5 muffins, how much do we need (x) to get to 34 muffins (2 per student):
x + 5 = 34
To solve for x, we type this equation into our search engine and we get:
x = [B]29[/B]
You are given a choice of taking the simple interest on $100,000 invested for 5 years at a rate of 2You are given a choice of taking the simple interest on $100,000 invested for 5 years at a rate of 2% or the interest on $100,000 invested for 5 years at an interest rate of 2% compounded daily. Which investment earns the greater amount of interest? Give the difference between the amounts of interest earned by the two investments
[URL='http://www.mathcelebrity.com/simpint.php?av=&p=100000&int=2&t=5&pl=Simple+Interest']Simple interest balance after 5 years[/URL] at 2% is $110,000.
[URL='http://www.mathcelebrity.com/compoundint.php?bal=100000&nval=1825&int=2&pl=Daily']Daily compounded interest for 5 years[/URL] at 2% is 365 days per year * 5 years = 1,825 days = [B]$110,516.79
Compound interest earns more by $110,516.79 - $110,000 = $516.79[/B]
You are purchasing carpeting for an office building. The space to be carpeted is 30 feet by 50 feet.You are purchasing carpeting for an office building. The space to be carpeted is 30 feet by 50 feet. Company A charges $2.99 per square foot plus a $200 installation charge. Company B charges $19.99 per square yard plus a $500 installation charge. What is the best deal?
Did you notice the word snuck in on this problem? Company B is given in square [I][B]yards[/B][/I], not feet. Let's convert their price to square feet to match company A.
[U]Company B conversion:[/U]
Since we have 1 square yard = 3 feet * 3 feet = 9 square feet, we need to solve the following proportion:
$19.99/square yard * 1 square yard/9 feet = $19.99 square yard / 9 feet = $2.22 / square foot.
Now, let's set up the cost equations C(s) for each Company in square feet (s)
[LIST]
[*]Company A: C(s) = 200 + 2.99s
[*]Company B: C(s) = 500 + 2.22s
[/LIST]
The problem asks for s = 30 feet * 50 feet = 1500 square feet. So we want to calculate C(1500)
[U]Company A:[/U]
C(1500) = 200 + 2.99(1500)
C(1500) = 200 + 4485
C(1500) = 4685
[U]Company B:[/U]
C(1500) = 500 + 2.22(1500)
C(1500) = 500 + 3330
C(1500) = 3830
Since [B]Company B[/B] has the lower cost per square foot, they are the better buy.
You buy a container of cat litter for $12.25 and a bag of cat food for x dollars. The total purchaseYou buy a container of cat litter for $12.25 and a bag of cat food for x dollars. The total purchase is $19.08, which includes 6% sales tax. Write and solve an equation to find the cost of the cat food.
Our purchase includes at cat litter and cat food. Adding those together, we're given:
12.25 + x = 19.08
To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=12.25%2Bx%3D19.08&pl=Solve']we type this equation into our search engine[/URL], and we get:
x = 6.83
Since the cat food includes sales tax, we need to remove the sales tax of 6% to get the original purchase price.
Original purchase price = After tax price / (1 + tax rate)
Original purchase price = 6.83/1.06
Original purchase price = [B]$6.44[/B]
You can spend at most $35. If you buy 5 tickets, how much can you spend on each ticketYou can spend at most $35. If you buy 5 tickets, how much can you spend on each ticket
We're given the number of tickets as 5.
We know cost = price * quantity
Let p = price
The phrase [B]at most[/B] means less than or equal to, so we have:
5p <= 35
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=5p%3C%3D35&pl=Show+Interval+Notation']Plugging this inequality into our search engine[/URL], we have:
[B]p <= 7[/B]
You choose an alpha level of .01 and then analyze your data.
(a) What is the probability thatYou choose an alpha level of .01 and then analyze your data.
(a) What is the probability that you will make a Type I error given that the null hypothesis is true?
(b) What is the probability that you will make a Type I error given that the null hypothesis is false.
[B](a) 0.01. Instead, α is the probability of a Type I error given that the null hypothesis is true. If the null hypothesis is false, then it is impossible to make a Type I error.[/B]
[B](b) Impossible Instead, α is the probability of a Type I error given that the null hypothesis is true. If the null hypothesis is false, then it is impossible to make a Type I error.[/B]
You deposit $2000 in an account that earns simple interest at an annual rate of 4%. How long must yoYou deposit $2000 in an account that earns simple interest at an annual rate of 4%. How long must you leave the money in the account to earn $500 in interest?
The simple interest formula for the accumulated balance is:
Prt = I
We are given P = 2,000, r = 0.04, and I = 500.
2000(0.04)t = 500
80t = 500
Divide each side by 80
t = [B]6.25 years
[MEDIA=youtube]Myz0FZgwZpk[/MEDIA][/B]
You deposit $750 in an account that earns 5% interest compounded quarterly. Show and solve a functioYou deposit $750 in an account that earns 5% interest compounded quarterly. Show and solve a function that represents the balance after 4 years.
The Accumulated Value (A) of a Balance B, with an interest rate per compounding period (i) for n periods is:
A = B(1 + i)^n
[U]Givens[/U]
[LIST]
[*]4 years of quarters = 4 * 4 = 16 quarters. So this is t.
[*]Interest per quarter = 5/4 = 1.25%
[*]Initial Balance (B) = 750.
[/LIST]
Using our [URL='https://www.mathcelebrity.com/compoundint.php?bal=750&nval=16&int=5&pl=Quarterly']compound balance interest calculator[/URL], we get the accumulated value A:
[B]$914.92[/B]
You earned $141 last week babysitting and cleaning. You earned $5 per hour babysitting and $7 per hoYou earned $141 last week babysitting and cleaning. You earned $5 per hour babysitting and $7 per hour cleaning. You worked 9 more hours babysitting than cleaning. How many hours did you work last week?
Let b be the hours of babysitting and c be the hours of cleaning. We're given two equations:
[LIST=1]
[*]b = c + 9
[*]5b + 7c = 141
[/LIST]
Substitute equation (1) into (2):
5(c + 9) + 7c = 141
Multiply through:
5c + 45 + 7c = 141
Combine like terms:
12c + 45 = 141
[URL='https://www.mathcelebrity.com/1unk.php?num=12c%2B45%3D141&pl=Solve']Typing this equation into our search engine[/URL], we get:
c = 8
Now substitute this value of c back into Equation (1):
b = 8 + 9
b = 17
The total hours worked (t) is:
t = b + c
t = 17 + 8
t = [B]25[/B]
You have $80. Jeans cost $29 and shirts cost $12. Mom told you to buy one pair of jeans and use theYou have $80. Jeans cost $29 and shirts cost $12. Mom told you to buy one pair of jeans and use the rest of the money to buy shirts. Find the inequality.
Let j be the number of jeans. Let s be the number of shirts. We are given:
[LIST]
[*]Mom told you to buy one pair of jeans. So we have $80 to start with - $29 for 1 pair of jeans = $51 left over
[/LIST]
Now, since shirts cost $12 each, and our total number of shirts we can buy is s, our inequality is [B]12s <= 51[/B].
We want to find the s that makes this inequality true.
[URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=12s%3C%3D51&pl=Show+Interval+Notation']Run this statement through our calculator[/URL], and we get s <= 4.25. But, we need s to be an integer, so we have s <= 4.
You roll a red die and a green die. What is the size of the sample space of all possible outcomes ofYou roll a red die and a green die. What is the size of the sample space of all possible outcomes of rolling these two dice, given that the red die shows an even number and the green die shows an odd number greater than 1?
[LIST]
[*]Red Die Sample Space {2, 4, 6}
[*]Green Die Sample Space {3, 5}
[*]Total Sample Space {(2, 3), (2, 5), (4, 3), (4, 5), (6, 3), (6, 5)}
[*]The sie of this is 6 elements.
[/LIST]
You spend $91 shopping for new clothes. You spend $24 for a pair of jeans and 35$ for a pair of shoeYou spend $91 shopping for new clothes. You spend $24 for a pair of jeans and 35$ for a pair of shoes. You also buy 4 shirts that cost d dollars. How much is each shirt?
Subtract the cost of the jeans and shoes to get the cost of the shirts:
Cost of shirts = Shopping Spend - Cost of Jeans - Cost of Shoes
Cost of shirts = $91 - $24 - $35
Cost of shirts = $32
We're given the cost of each shirt is s, and we bought 4 shirts. Therefore, we have:
4s = 32
[URL='https://www.mathcelebrity.com/1unk.php?num=4s%3D32&pl=Solve']Type this equation into the search engine[/URL], and we get the cost of each shirt s = [B]$8[/B]
Your friends in class want you to make a run to the vending machine for the whole group. Everyone piYour friends in class want you to make a run to the vending machine for the whole group. Everyone pitched in to make a total of $12.50 to buy snacks. The fruit drinks are $1.50 and the chips are $1.00. Your friends want you to buy a total of 10 items. How many drinks and how many chips were you able to purchase?
Let c be the number of chips. Let f be the number of fruit drinks. We're given two equations:
[LIST=1]
[*]c + f = 10
[*]c + 1.5f = 12.50
[/LIST]
Rearrange equation 1 by subtracting f from both sides:
[LIST=1]
[*]c = 10 - f
[*]c + 1.5f = 12.50
[/LIST]
Substitute equation (1) into equation (2):
10 - f + 1.5f = 12.50
To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=10-f%2B1.5f%3D12.50&pl=Solve']type this equation into our search engine[/URL] and we get:
[B]f = 5[/B]
Now, substitute this f = 5 value back into modified equation (1) above:
c = 10 - 5
[B]c = 5[/B]
Your grade must be at least 60 to pass this classYour grade must be at least 60 to pass this class
Assumptions and givens:
[LIST]
[*]The phrase [I]at least[/I] means greater than or equal to.
[*]Let g be your grade
[/LIST]
We have:
[B]g >= 60[/B]
Your mother gave you $13.32 With which to buy a present. This covered 3/5 of the cost. How much didYour mother gave you $13.32 With which to buy a present. This covered 3/5 of the cost. How much did the present cost
Let the present cost p. We set up the equation we're given:
3/5p = 13.32
[URL='https://www.mathcelebrity.com/1unk.php?num=3%2F5p%3D13.32&pl=Solve']Type this equation into our search engine[/URL] and we get:
p = [B]$22.20[/B]
Your profit for mowing lawns this week is $24. You are paid $8 per hour and you paid $40 for gas forYour profit for mowing lawns this week is $24. You are paid $8 per hour and you paid $40 for gas for the lawn mower. How many hours did you work this week?
We know profit from the equation below:
Revenue - Cost = Profit
We're given Profit as 42, so we have:
Revenue - Cost = 42
Let hours worked be h. We have revenue as:
Revenue = 8h
Cost = 40, so we plug these into profit to get:
8h - 40 = 42
To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=8h-40%3D42&pl=Solve']plug this equation into our math engine[/URL] and get:
h = [B]10.25[/B]
Z Score LookupFree Z Score Lookup Calculator - Given a Z-score probability statement from the list below, this will determine the probability using the normal distribution z-table.
* P(z < a)
* P(z <= a)
* P(z > a)
* P(z >= a)
* P(a < z < b)
Calculates z score probability
z varies jointly as x and y. If z=3 when x=3 and y=15, find z when x=6 and y=9z varies jointly as x and y. If z=3 when x=3 and y=15, find z when x=6 and y=9
Varies jointly means there exists a constant k such that:
z = kxy
We're given z = 3 when x = 3 and y = 15, so we have:
3 = 15 * 3 * k
3 = 45k
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=3%3D45k&pl=Solve']equation solver,[/URL] we see that:
k = 1/15
So our joint variation equation is:
z = xy/15
Then we're asked to find z when x = 6 and y = 9
z = 6 * 9 / 15
z = 54/15
[URL='https://www.mathcelebrity.com/search.php?q=54%2F15&x=0&y=0']z =[/URL] [B]18/5[/B]
Zalika thinks of a number. She subtracts 6 then multiplies the result by 5. The answer is the same aZalika thinks of a number. She subtracts 6 then multiplies the result by 5. The answer is the same as subtracting 5 from the number then multiplying by 4.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x. We're given two expressions in relation to this number (x):
[U]She subtracts 6 then multiplies the result by 5[/U]
[LIST]
[*]Subtract 6: x - 6
[*]Multiply the result by 5: 5(x - 6)
[/LIST]
[U]She subtracts 5 from the number then multiplying by 4[/U]
[LIST]
[*]Subtract 6: x - 5
[*]Multiply the result by 5: 4(x - 5)
[/LIST]
Finally, the expression [I]is the same as[/I] means an equation, so we set the first expression equal to the second expression to make the following equation:
5(x - 6) = 4(x - 5)
Now, let's solve the equation for x. To do this, we [URL='https://www.mathcelebrity.com/1unk.php?num=5%28x-6%29%3D4%28x-5%29&pl=Solve']type this equation into our search engine [/URL]and we get:
x = [B]10[/B]
Zero-Coupon Bond PriceFree Zero-Coupon Bond Price Calculator - This calculator calculates the price of a zero-coupon bond given a face value, yield rate, and term.
