134 results

%60 of the freshman ate pizza at lunch today. If 180 freshman ate pizza, how many freshman are enro

60% of the freshman ate pizza [URL='http://www.mathcelebrity.com/community/x-apple-data-detectors://3']at lunch today[/URL]. If 180 freshman ate pizza, how many freshman are enrolled at our school?
60% of x = 180
We write this as 0.6x = 180
Divide each side by 0.6 to isolate x.
We get x = 300 freshman

1 out of 12 homes is heated by fuel oil. At this rate, how many homes in a community of 36,000 homes

1 out of 12 homes is heated by fuel oil. At this rate, how many homes in a community of 36,000 homes are heated by fuel oil?
1/12 * 36000 = [B]3,000 homes[/B]

14 oranges $3.78

14 oranges $3.78
Using our [URL='http://www.mathcelebrity.com/unit-cost-calculator.php?num=14orangesfor3.78&pl=Calculate+Unit+Cost']unit cost calculator[/URL], we get:
[B]$0.27 per orange[/B].
You could also enter in the search engine:
14 oranges for $3.78

3 pound bag for $11.25

We need to find the unit cost, which is the cost of one unit of measurement.
The measurement unit is in pounds.
If it costs $11.25 for a 3 pound bag, how much is it per pound?
$11.25/3 = $3.75 per pound.

3 pound bag for $11.25

A new [URL='http://www.mathcelebrity.com/unit-cost-calculator.php']unit cost calculator[/URL] has been created.

3.50 per pound. you bought 18.25 worth of strawberries

3.50 per pound. you bought 18.25 worth of strawberries
The question asks for unit cost.
Unit Cost = Total Cost / Total Quantity
Unit Cost = 18.25 / 3.50
Unit Cost = [B]5.21[/B]

4 cans for $2.48 how much does 1 can cost?

4 cans for $2.48 how much does 1 can cost?
[URL='https://www.mathcelebrity.com/unit-cost-calculator.php?num=4cansfor2.48&pl=Calculate+Unit+Cost']Using our unit cost calculator[/URL], we get:
1 can is [B]$0.62[/B]

A 12% acid solution is made by mixing 8% and 20% solutions. If the 450 ml of the 12% solution is req

A 12% acid solution is made by mixing 8% and 20% solutions. If the 450 ml of the 12% solution is required, how much of each solution is required?
Component Unit Amount
8% Solution: 0.08 * x = 0.08x
20% Solution: 0.2 * y = 0.2y
12% Solution: 0.12 * 450 = 54
We add up the 8% solution and 20% solution to get two equations:
[LIST=1]
[*]0.08x + 0.2y = 54
[*]x + y = 450
[/LIST]
We have a simultaneous set of equations. We can solve it using three methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.08x+%2B+0.2y+%3D+54&term2=x+%2B+y+%3D+450&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.08x+%2B+0.2y+%3D+54&term2=x+%2B+y+%3D+450&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.08x+%2B+0.2y+%3D+54&term2=x+%2B+y+%3D+450&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
[LIST]
[*][B]x = 300 ml[/B]
[*][B]y = 150 ml[/B]
[/LIST]

A book publishing company has fixed costs of $180,000 and a variable cost of $25 per book. The books

A book publishing company has fixed costs of $180,000 and a variable cost of $25 per book. The books they make sell for $40 each.
[B][U]Set up Cost Function C(b) where b is the number of books:[/U][/B]
C(b) = Fixed Cost + Variable Cost x Number of Units
C(b) = 180,000 + 25(b)
[B]Set up Revenue Function R(b):[/B]
R(b) = 40b
Set them equal to each other
180,000 + 25b = 40b
Subtract 25b from each side:
15b = 180,000
Divide each side by 15
[B]b = 12,000 for break even[/B]

A cellular offers a monthly plan of $15 for 350 min. Another cellular offers a monthly plan of $20 f

A cellular offers a monthly plan of $15 for 350 min. Another cellular offers a monthly plan of $20 for 425 min. Which company offers the better plan?
Let's figure out the unit cost of minutes per dollar:
[LIST=1]
[*]Plan 1: 350 minutes / $15 = 23.33 minutes per dollar
[*]Plan 2: 425 minutes / $20 = 21.25 minutes per dollar
[/LIST]
[B]Plan 2 is better, because you get more minutes per dollar.[/B]

A company has a fixed cost of $34,000 and a production cost of $6 for each unit it manufactures. A u

A company has a fixed cost of $34,000 and a production cost of $6 for each unit it manufactures. A unit sells for $15
Set up the cost function C(u) where u is the number of units is:
C(u) = Cost per unit * u + Fixed Cost
C(u) = [B]6u + 34000[/B]
Set up the revenue function R(u) where u is the number of units is:
R(u) = Sale price per unit * u
R(u) = [B]15u[/B]

a company has revenue given by R(x)=500x dollars and total cost given by C(x)=48,000 100x dollars, w

a company has revenue given by R(x)=500x dollars and total cost given by C(x)=48,000 + 100x dollars, where x is the number of units produced and sold. How many units will give a profit
Profit P(x) is given by:
R(x) - C(x)
So we have:
P(x) = 500x - (100x + 48,000)
P(x) = 500x - 100x - 48,000
P(x) = 400x - 48,000
A profit is found when P(x) > 0, so we have:
400x - 48000 > 0
To solve this inequality, [URL='https://www.mathcelebrity.com/1unk.php?num=400x-48000%3E0&pl=Solve']we type it into our search engine [/URL]and we get:
[B]x > 120[/B]

A company is planning to manufacture a certain product. The fixed costs will be $474778 and it will

A company is planning to manufacture a certain product. The fixed costs will be $474778 and it will cost $293 to produce each product. Each will be sold for $820. Find a linear function for the profit, P , in terms of units sold, x .
[U]Set up the cost function C(x):[/U]
C(x) = Cost per product * x + Fixed Costs
C(x) = 293x + 474778
[U]Set up the Revenue function R(x):[/U]
R(x) = Sale Price * x
R(x) = 820x
[U]Set up the Profit Function P(x):[/U]
P(x) = Revenue - Cost
P(x) = R(x) - C(x)
P(x) = 820x - (293x + 474778)
P(x) = 820x - 293x - 474778
[B]P(x) = 527x - 474778[/B]

A companys cost function is C(x) = 16x2 + 900 dollars, where x is the number of units. Find th

A companys cost function is C(x) = 16x^2 + 900 dollars, where x is the number of units. Find the marginal cost function.
Marginal Cost is the derivative of the Cost function.
[B]C'(x) = 32x[/B]

A construction crew must build a road in 10 months or they will be penalized $500,000. It took 10 wo

A construction crew must build a road in 10 months or they will be penalized $500,000. It took 10 workers 6 months to build half of the road. How many additional workers must be added to finish the road in the remaining 4 months?
Calculate unit rate per one worker:
10 workers * 6 months = 60 months for one worker
Calculate workers needed:
60 months / 4 months = 15 workers
Calculate additional workers needed:
Additional workers needed = New workers needed - Original workers needed
Additional workers needed = 15 - 10
Additional workers needed = [B]5 additional workers[/B]

A department store buys 100 shirts at a cost of $600 and sells them at a selling price of 10 each fi

A department store buys 100 shirts at a cost of $600 and sells them at a selling price of 10 each find the percentage mark up
Find Unit Cost:
Unit Cost = Cost / Number of Shirts
Unit Cost = 600 / 100
Unit Cost = 6
With a selling price of 10, our markup percentage is:
Markup % = 100 * (New Price - Old Price)/Old Price
Markup % = 100 * (10 - 6)/6
Markup % = 100 * 4/6
Markup % = 400/6
Markup % = [B]66.67%[/B]

A gallon of milk sells for $3.09 and a quart of milk sells for $0.80.

A gallon of milk sells for $3.09 and a quart of milk sells for $0.80.
Let's get this in terms of a common measurement for unit cost. Let's use gallons:
1 gallon = 4 quarts
Gallon of milk
$3.09 / gallon
Quart of milk
0.80 / 0.25 gallons
Multiply top and bottom by 4:
$3.20 / gallon
[B]This means the gallon is the better buy[/B]

A grocery store is selling 6 cans of cat food for $3. Find the cost of a can of cat food

A grocery store is selling 6 cans of cat food for $3. Find the cost of a can of cat food
Unit Cost = Cost / Quantity
Unit Cost = $3 / 6
Unit cost = [B]0.50 per can[/B]

A grocery store sells 6 pounds of apples for $12. What is the unit price of the apples?

A grocery store sells 6 pounds of apples for $12. What is the unit price of the apples?
Unit Price = Cost/Quantity
Unit Price = 12/6
[B]Unit Price = $2/lb[/B]

A grocery store sells a bag of six oranges for $2.34 if Nova spends $1.95 on oranges how many did sh

A grocery store sells a bag of six oranges for $2.34 if Nova spends $1.95 on oranges how many did she buy
Unit cost is:
2.34/6 = 0.39 cents each
Nova spent $1.95
$1.95/0.39 = [B]5 oranges[/B]

A gym membership has a $50 joining fee plus charges $17 a month for m months

A gym membership has a $50 joining fee plus charges $17 a month for m months
Build a cost equation C(m) where m is the number of months of membership.
C(m) = Variable Cost * variable units + Fixed Cost
C(m) = Months of membership * m + Joining Fee
Plugging in our numbers and we get:
[B]C(m) = 17m + 50
[MEDIA=youtube]VGXeqd3ikAI[/MEDIA][/B]

a kilo of grapes costs 200.50 how much will you pay if you buy 3 kilos

a kilo of grapes costs 200.50 how much will you pay if you buy 3 kilos
Total Amount = Cost per unit * Quantity
Total Amount = 200.50 * 3
Total Amount = [B]$601.50[/B]

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $10 for each unit produ

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $10 for each unit produced. The product sells for $22/unit.
The cost function for each unit u is:
C(u) = Variable Cost * Units + Fixed Cost
C(u) = 10u + 100000
The revenue function R(u) is:
R(u) = 22u
We want the break-even point, which is where:
C(u) = R(u)
10u + 100000 = 22u
[URL='https://www.mathcelebrity.com/1unk.php?num=10u%2B100000%3D22u&pl=Solve']Typing this equation into our search engine[/URL], we get:
u =[B]8333.33[/B]

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $12 for each unit produ

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $12 for each unit produced. The product sells for $20/unit
[U]Cost Function C(u) where u is the number of units:[/U]
C(u) = cost per unit * u + fixed cost
C(u) = 12u + 100000
[U]Revenue Function R(u) where u is the number of units:[/U]
R(u) = Sale price * u
R(u) = 20u
Break even point is where C(u) = R(u):
C(u) = R(u)
12u + 100000 = 20u
To solve for u, we [URL='https://www.mathcelebrity.com/1unk.php?num=12u%2B100000%3D20u&pl=Solve']type this equation into our search engine[/URL] and we get:
u = [B]12,500[/B]

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $14 for each unit produ

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $14 for each unit produced. The product sells for $20/unit.
Let u be the number of units. We have a cost function C(u) as:
C(u) = Variable cost * u + Fixed Cost
C(u) = 14u + 100000
[U]We have a revenue function R(u) with u units as:[/U]
R(u) = Sale Price * u
R(u) = 20u
[U]We have a profit function P(u) with u units as:[/U]
Profit = Revenue - Cost
P(u) = R(u) - C(u)
P(u) = 20u - (14u + 100000)
P(u) = 20u - 14u - 100000
P(u) = 6u - 1000000

A manufacturer has a monthly fixed cost of $25,500 and a production cost of $7 for each unit produce

A manufacturer has a monthly fixed cost of $25,500 and a production cost of $7 for each unit produced. The product sells for $10/unit.
Set up cost function where u equals each unit produced:
C(u) = 7u + 25,500
Set up revenue function
R(u) = 10u
Break Even is where Cost equals Revenue
7u + 25,500 = 10u
Plug this into our [URL='http://www.mathcelebrity.com/1unk.php?num=7u%2B25500%3D10u&pl=Solve']equation calculator[/URL] to get [B]u = 8,500[/B]

A manufacturer has a monthly fixed cost of $52,500 and a production cost of $8 for each unit produce

A manufacturer has a monthly fixed cost of $52,500 and a production cost of $8 for each unit produced. The product sells for $13/unit.
Using our [URL='http://www.mathcelebrity.com/cost-revenue-profit-calculator.php?fc=52500&vc=8&r=13&u=20000%2C50000&pl=Calculate']cost-revenue-profit calculator[/URL], we get the following:
[LIST]
[*]P(x) = 55x - 2,500
[*]P(20,000) = 47,500
[*]P(50,000) = 197,500
[/LIST]

A pack of 36 black sharp tip markers costs $34.49. What is the price of one marker?

A pack of 36 black sharp tip markers costs $34.49. What is the price of one marker?
Set up unit cost:
34.49/36 = [B]$0.96 per marker[/B]

A plane is flying at an altitude of 45,000 feet. It begins to drop in altitude 3,000 feet per minute

A plane is flying at an altitude of 45,000 feet. It begins to drop in altitude 3,000 feet per minute. What is the slope in this situation?
Set up a graph where minutes is on the x-axis and altitude is on the y-axis.
[LIST=1]
[*]Minute 1 = (1, 42,000)
[*]Minute 2 = (2, 39,000)
[*]Minute 3 = (3, 36,000)
[*]Minute 4 = (4, 33,000)
[/LIST]
You can see for every 1 unit move in x, we get a -3,000 unit move in y.
Pick any of these 2 points, and [URL='https://www.mathcelebrity.com/slope.php?xone=1&yone=42000&slope=+2%2F5&xtwo=2&ytwo=39000&bvalue=+&pl=You+entered+2+points']use our slope calculator[/URL] to get:
Slope = -[B]3,000[/B]

A researcher posed a null hypothesis that there was no significant difference between boys and girls

A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 120 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5.0. The mean score for boys was 65 and the standard deviation of mean was 6.0. What's the absolute value of the difference between means?
|70 -65| = |5| = 5

A researcher posed a null hypothesis that there was no significant difference between boys and girls

A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 100 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5.0. The mean score for boys was 65 and the standard deviation of mean was 5.0. What is the standard error of the difference in means?
[B]0.707106781187[/B] using our [URL='http://www.mathcelebrity.com/meandiffconf.php?n1=+100&xbar1=70&stdev1=5&n2=+100&xbar2=65&stdev2=5&conf=+99&pl=Hypothesis+Test']difference of means calculator[/URL]

A researcher posed a null hypothesis that there was no significant difference between boys and girls

A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. He randomly sampled 100 girls and 100 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5.0. The mean score for boys was 65 and the standard deviation of mean was 5.0. What's the t-value (two-tailed) for the null hypothesis that boys and girls have the same test scores?
t = 7.07106781187 using our [URL='http://www.mathcelebrity.com/meandiffconf.php?n1=+100&xbar1=70&stdev1=5&n2=+100&xbar2=65&stdev2=5&conf=+99&pl=Hypothesis+Test']difference of means calculator[/URL]

a roller coaster has 6 trains. each train has 3 cars, and each car seats 4 people. write and simplif

a roller coaster has 6 trains. each train has 3 cars, and each car seats 4 people. write and simplify an expression including units to find the total number of people that can ride the roller coaster at one time
6 trains * 3 cars per train * 4 people per car = [B]72 people[/B]

A Sales Manager buys antacid in bottles by the gross. If he goes through 3 bottles of antacid everyd

A Sales Manager buys antacid in bottles by the gross. If he goes through 3 bottles of antacid everyday, how long will the gross last?
[U][B]Calculate a gross[/B][/U]
[URL='https://en.wikipedia.org/wiki/Gross_(unit)#:~:text=A%20gross%20refers%20to%20a,cubic%20dozen%2C%20123).']A gross equals[/URL] 144 because 1 gross = 12 dozen
12 dozen * 12 items/dozen = 144
[B]
[U]Answer[/U][/B]
Days lasted = Total Bottles / Bottles per day
Days lasted = 144 bottles / 3 days
[B]Days lasted = 48 days[/B]

A Septonian won the lottery in the United States and won $1,000,000. How many dollars in that in bas

A Septonian won the lottery in the United States and won $1,000,000. How many dollars in that in base 7?
Using our [URL='https://www.mathcelebrity.com/binary.php?num=1000000&check1=7&bchoice=7&pl=Convert']base change calculator[/URL], we get:
1,000,000 in base 7 = [B]11,333,311[/B]

A set of 6 wooden chairs costs $444. A set of 8 metal chairs costs $720. How much more do the metal

A set of 6 wooden chairs costs $444. A set of 8 metal chairs costs $720. How much more do the metal chairs cost per chair?
[U]Wooden Chair Unit Cost:[/U]
Unit Cost = Total Cost / Quantity
Unit Cost = 444/6
Unit Cost = 74
[B][/B]
[U]Metal Chair Unit Cost:[/U]
Unit Cost = Total Cost / Quantity
Unit Cost = 720/8
Unit Cost = 90
[B][B][/B][/B]
Find the difference (how much more)
Difference = Metal Chair Unit Cost - Wooden Chair Unit Cost
Difference = 90 - 74
Difference = [B]16[/B]

A shoe store was having a sale where 2 pairs of Brand A shoes cost $23.10 and 3 pairs of Brand B sho

A shoe store was having a sale where 2 pairs of Brand A shoes cost $23.10 and 3 pairs of Brand B shoes cost $35.85. Which brand is the better buy?
[URL='https://www.mathcelebrity.com/betterbuy.php?p1=23.10&p2=35.85&q1=2&q2=3&pl=Better+Buy']Using our better buy calculator[/URL]:
[SIZE=5][B]Calculate Unit Price[/B][/SIZE]
Unit Price = Price/Quantity
[SIZE=5][B]Calculate Unit Price 1:[/B][/SIZE]
Unit Price Brand A = P1/Q1
Unit Price Brand A = 23.10/2
Unit Price Brand A = 11.55
[SIZE=5][B]Calculate Unit Price 2:[/B][/SIZE]
Unit Price Brand B = P2/Q2
Unit Price Brand B = 35.85/3
Unit Price Brand B = 11.95
Since Brand A's Unit price is lower, [B]Brand A is the better buy
[MEDIA=youtube]Q16iZn6Uer8[/MEDIA][/B]

a store buys 48 candy bars. they sell the candy for .75 each

a store buys 48 candy bars. they sell the candy for .75 each
Revenue = Cost per unit * # of Units
Revenue = 0.75 * 48
Revenue = [B]36[/B]

A student and the marine biologist are together at t = 0. The student ascends more slowly than the m

A student and the marine biologist are together at t = 0. The student ascends more slowly than the marine biologist. Write an equation of a function that could represent the student's ascent. Please keep in mind the slope for the marine biologist is 12.
Slope means rise over run.
In this case, rise is the ascent distance and run is the time.
12 = 12/1, so for each second of time, the marine biologist ascends 12 units of distance
If the student ascends slower, than the total distance gets reduced by an unknown factor, let's call it c. So we have the student's ascent function as:
[B]y(t) = 12t - c[/B]

Activity Method Depreciation

Free Activity Method Depreciation Calculator - Calculates the following:
Depreciable Base, Depreciation per Unit, Depreciation for Period

alex burns approximately 650 calories in a 1.25-hour game. Daniellle enjoys kickboxing and burns app

alex burns approximately 650 calories in a 1.25-hour game. Daniellle enjoys kickboxing and burns approximately 420 calories in 45 minute class. who burns calories at the higher rate?
We want a calories to minutes measure.
[LIST]
[*][URL='https://www.mathcelebrity.com/timecon.php?quant=1.25&pl=Calculate&type=hour']1.25 hours[/URL] = 75 minutes
[/LIST]
Alexa's unit calorie burn:
650/75 = 8.67
Danielle's unit calorie burn:
420/45 = 9.33
So [B]Danielle[/B] burns calories at a higher rate.

Alonzo needs to buy some pencils. Brand A has a pack of 36 pencils for $8.52. Brand B has a pack of

Alonzo needs to buy some pencils. Brand A has a pack of 36 pencils for $8.52. Brand B has a pack of 48 pencils for $9.98. Find the unit price for each brand. Then state which brand is the better buy based on the unit price. Round your answers to the nearest cent.
Using our [URL='http://www.mathcelebrity.com/betterbuy.php?p1=8.52&p2=9.98&q1=36&q2=48&pl=Better+Buy']better buy calculator[/URL], we see the following unit prices:
[LIST]
[*][B]Brand A = $0.24[/B]
[*][B]Brand B = $0.21[/B].
[*][B]Brand B has the better unit price by 3 cents.[/B]
[/LIST]

Angelica’s financial aid stipulates that her tuition cannot exceed $1000. If her local community col

Angelica’s financial aid stipulates that her tuition cannot exceed $1000. If her local community college charges a $35 registration fee plus $375 per course, what is the greatest number of courses for which Angelica can register?
We set up the Tuition function T(c), where c is the number of courses:
T(c) = Cost per course * c + Registration Fee
T(c) = 35c + 375
The problem asks for the number of courses (c) where her tuition [I]cannot exceed[/I] $1000. The phrase [I]cannot exceed[/I] means less than or equal to, or no more than. So we setup the inequality for T(c) <= 1000 below:
35c + 375 <= 1000
To solve this inequality for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=35c%2B375%3C%3D1000&pl=Solve']type it in our search engine and we get[/URL]:
c <= 17.85
Since we cannot have fractional courses, we round down and get:
c[B] <= 17[/B]

Anna paints a fence in 4 hours wile her brother paints it in 5 hours. If they work together, how lon

Anna paints a fence in 4 hours wile her brother paints it in 5 hours. If they work together, how long will it take them to paint the fence?
Set up unit rates per hour:
[LIST]
[*]Anna paints 1/4 of a fence per hour
[*]Brother paints 1/5 of a fence per hour
[*]Combined, they paint [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F4&frac2=1%2F5&pl=Add']1/4 + 1/5[/URL] = 9/20 of a fence per hour
[/LIST]
Setup a proportion of time to hours where h is the number of hours needed to paint the fence
9/20 of a fence the first hour
18/20 of a fence the second hour
2/20 is left. Each 1/20 of the fence takes 60/9 = 6 & 2/3 minutes
6 & 2/3 minutes * 2 = 13 & 1/3 minutes
Final time is:
[B]2 hours and 13 & 1/3 minutes[/B]

at a bakery the cost of one cupcake and 2 slices of pie is $12.40. the cost of 2 cupcakes and 3 slic

at a bakery the cost of one cupcake and 2 slices of pie is $12.40. the cost of 2 cupcakes and 3 slices of pie costs $20.20. what is the cost of one cupcake?
Let the number of cupcakes be c
Let the number of pie slices be p
Total Cost = Unit cost * quantity
So we're given two equations:
[LIST=1]
[*]1c + 2p = 12.40
[*]2c + 3p = 20.20
[/LIST]
We can solve this system of equations any one of three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1c+%2B+2p+%3D+12.40&term2=2c+%2B+3p+%3D+20.20&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1c+%2B+2p+%3D+12.40&term2=2c+%2B+3p+%3D+20.20&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1c+%2B+2p+%3D+12.40&term2=2c+%2B+3p+%3D+20.20&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
[LIST]
[*][B]c = 3.2[/B]
[*]p = 4.6
[/LIST]

At Sams Club, 32 cans of Coke cost a total of $8.96. What is the cost per can?

At Sams Club, 32 cans of Coke cost a total of $8.96. What is the cost per can?
Unit Cost is Total Cost / Number of Units
Unit Cost = $8.96/32
Unit Cost = [B]$0.28[/B]

Better Buy Comparison

Free Better Buy Comparison Calculator - Given two items with a price and quantity, this determines which is the better buy by comparing unit prices. Finds the better deal.

Brandon can shovel his sidewalk in 8 minutes, while his brother can shovel the walk in 12 minutes. I

Brandon can shovel his sidewalk in 8 minutes, while his brother can shovel the walk in 12 minutes. If they work together, how long will it take them to shovel the sidewalk?
Set up unit rates:
[LIST]
[*]Brandon can shovel 1/8 of a sidewalk per minute
[*]His brother can shovel 1/12 of a sidewalk per minute
[/LIST]
Together, they can shovel:
[URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F8&frac2=1%2F12&pl=Add']1/8 + 1/12[/URL] = 5/24 of a sidewalk per minute
1 minute = 60 seconds
5/24 / 60 seconds = 1/x seconds
5/24 * 60 = 1/x
5/1440 = 1/x
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=5&num2=1&den1=1440&den2=x&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
x = 288
288/60 = [B]4 minutes and 48 seconds[/B]

Carly grew 50 plants with 25 seed packets. With 37 seed packets, how many total plants can Carly hav

Carly grew 50 plants with 25 seed packets. With 37 seed packets, how many total plants can Carly have in her backyard? Solve using unit rates.
Set up a proportion of plants per seed packets where p is the number of plants per 37 seed packets.
50/25 = p/37
Copying and pasting this problem [URL='http://www.mathcelebrity.com/prop.php?num1=50&num2=p&den1=25&den2=37&propsign=%3D&pl=Calculate+missing+proportion+value']into our search engine[/URL], we get [B]p = 74[/B].

Cost Revenue Profit

Free Cost Revenue Profit Calculator - Given a total cost, variable cost, revenue amount, and profit unit measurement, this calculates profit for each profit unit

Date and Time Difference

Free Date and Time Difference Calculator - Calculates the difference between two dates using the following methods

1) Difference in dates using year/month/day/hour/minute/second as the primary unit of time

2) Difference in dates in the form of years remaining, months remaining, days remaining, hours remaining, minutes remaining, seconds remaining.

1) Difference in dates using year/month/day/hour/minute/second as the primary unit of time

2) Difference in dates in the form of years remaining, months remaining, days remaining, hours remaining, minutes remaining, seconds remaining.

Dave paints a fence in 4 hours while Sara paints the same fence in 2 hours. If they work together, h

Dave paints a fence in 4 hours while Sara paints the same fence in 2 hours. If they work together, how long will it take them to paint the fence?
Set up unit rates:
[LIST]
[*]Dave paints 1/4 of the fence in 1 hour
[*]Sara will paint 1/2 of the fence in 1 hour
[/LIST]
So together, they paint 1/2 + 1/4 = 2/4 + 14 = 3/4 of the fence in one hour.
1 hour = 60 minutes, so we set up a proportion of time to minutes where m is the time in minutes needed to complete 1 full fence:
3/4/60 = 1/m
3/240 = 1/m
[URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=3&num2=1&den1=240&den2=m&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion in our math engine[/URL], we get:
m = [B]80 minutes[/B]
[B]80 minutes is also 1 hour and 20 minutes.[/B]

Donna bought 4 bags of dog treats for $9.36. What is the cost per bag of dog treats?

Donna bought 4 bags of dog treats for $9.36. What is the cost per bag of dog treats?
Using our unit cost formula, we get:
$9.36/4
[B]$2.34 per bag[/B]

Donna buys a bag of 11 oranges for 2.86. Find the unit price in dollars per orange.

Set up a proportion in dollars to oranges
2.86/11 oranges = x/1
[URL='http://www.mathcelebrity.com/unit-cost-calculator.php?num=11poundbagfor2.86&pl=Calculate+Unit+Cost']Using our unit cost calculator[/URL]
[B]0.26 per orange[/B]

Dotty McGinnis starts up a small business manufacturing bobble-head figures of famous soccer players

Dotty McGinnis starts up a small business manufacturing bobble-head figures of famous soccer players. Her initial cost is $3300. Each figure costs $4.50 to make. a. Write a cost function, C(x), where x represents the number of figures manufactured.
Cost function is the fixed cost plus units * variable cost.
[B]C(x) = 3300 + 4.50x[/B]

Each unit on a map of a forest represents 1 mile. To the nearest tenth of a mile, what is the distan

Each unit on a map of a forest represents 1 mile. To the nearest tenth of a mile, what is the distance from a ranger station at (1, 2) on the map to a river crossing at (2, 4) ?
We use our 2 point calculator and we get a distance of 2.2361.
Since each unit represents 1 mile, we have:
2.2361 units * 1 mile per unit = [B]2.2361 miles[/B]

Find x

Find x
[IMG]https://mathcelebrity.com/community/data/attachments/0/cong-angles.jpg[/IMG]
Since both angles are congruent, we set them equal to each other:
6x - 20 = 4x
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=6x-20%3D4x&pl=Solve']type this equation into our math engine[/URL] and we get:
x = [B]10[/B]

Fixed cost 500 marginal cost 8 item sells for 30

fixed cost 500 marginal cost 8 item sells for 30.
Set up Cost Function C(x) where x is the number of items sold:
C(x) = Marginal Cost * x + Fixed Cost
C(x) = 8x + 500
Set up Revenue Function R(x) where x is the number of items sold:
R(x) = Revenue per item * items sold
R(x) = 30x
Set up break even function (Cost Equals Revenue)
C(x) = R(x)
8x + 500 = 30x
Subtract 8x from each side:
22x = 500
Divide each side by 22:
x = 22.727272 ~ 23 units for breakeven

Fractions

Free Fractions Calculator - Calculates things like fraction to percent, fraction to decimal, unit fraction, ratios, and more

Gigi’s family left their house and drove 14 miles south to a gas station and then 48 miles east to a

Gigi’s family left their house and drove 14 miles south to a gas station and then 48 miles east to a water park. How much shorter would their trip to the water park have been if they hadn’t stopped at the gas station and had driven along the diagonal path instead?
[IMG]https://mathcelebrity.com/community/data/attachments/0/pythag-diagonal.jpg[/IMG]
Using our [URL='https://www.mathcelebrity.com/pythag.php?side1input=14&side2input=48&hypinput=&pl=Solve+Missing+Side']Pythagorean theorem calculator[/URL], we see the diagonal route would be:
50 miles
The original trip distance was:
Original Trip Distance = 14 + 48
Original Trip Distance = 62 miles
Diagonal Trip was 50 miles, so the difference is:
Difference = Original Trip Distance - Diagonal Distance
Difference = 62 - 50
Difference = [B]12 miles[/B]

High and Low Method

Free High and Low Method Calculator - Calculates the variable cost per unit, total fixed costs, and the cost volume formula

High-Low Method

Free High-Low Method Calculator - Calculates Variable Cost per Unit, Total Fixed Cost, and Cost Volume using the High-Low Method

I sold 3 units in 563 attempts. How many did I sell per 100 attempts?

I sold 3 units in 563 attempts. How many did I sell per 100 attempts?
Set up a proportion of sales to attempts where s is the number of sales for 100 attempts:
3/563 = s/100
[URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=s&den1=563&den2=100&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this in our search engine[/URL], we get:
s = [B]0.532 sales[/B]

If .75 inches on a map are equal to 6 miles, how many miles is one inch equal to?

If .75 inches on a map are equal to 6 miles, how many miles is one inch equal to?
Using the unit measurement, we have:
6 miles / 0.75 inches = [B]8 miles per inch[/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 7 movie tickets cost $63 what is the unit price of the movie tickets?

If 7 movie tickets cost $63 what is the unit price of the movie tickets?
Unit Cost = Total Cost / Total Quantity
Unit Cost = 63/7
Unit Cost = [B]$9 per ticket[/B]

if hose a can fill up a swimming pool in 6 hours, hose b in 3 hours, hose c in 2 hours, how long wil

if hose a can fill up a swimming pool in 6 hours, hose b in 3 hours, hose c in 2 hours, how long will it take to fill up the pool using all 3 hoses?
Let V be the pool's Volume. Each hour, the hoses fill up this much of the pool:
[LIST]
[*]Hose A, V/6 of the pool
[*]Hose B, V/3 of the pool
[*]Hose C, V/2 of the pool
[/LIST]
Effective fill rate is:
V/6 + V/3 + V/2
6V/36 + 12V/36 + 18V/36
36V/36 which is volume units per hour
Let t = units / rate
t = 1 hour, so we have:
t = units / rate
t = V (volume units) / V (volume units / hour)
t = [B]1 hour[/B]

If Juan spent $1.28 for ground beef that cost $1.92 per pound, how much ground beef did Juan buy?

If Juan spent $1.28 for ground beef that cost $1.92 per pound, how much ground beef did Juan buy?
Calculate unit rate:
$1.28 / $1.92 per pound = [B]2/3 pound or 0.6667 pounds[/B]

If labor (x) costs $249 per unit, materials (y) cost $162 per unit, and capital (z) costs $ 7

If labor (x) costs $249 per unit, materials (y) cost $162 per unit, and capital (z) costs $ 77 per unit, write a function for total cost.
Total Cost = Labor Total Cost + Materials Total Cost + Capital Total Cost
Total Cost = [B]249x + 162y + 77z[/B]

If the cost of each hat is x dollars, what is the cost of y hats?

If the cost of each hat is [I]x[/I] dollars, what is the cost of [I]y[/I] hats?
Cost = Price per unit * Quantity
Cost = [B]xy dollars [/B]or [B]$xy[/B]

if the point (.53,y) is on the unit circle in quadrant 1, what is the value of y?

if the point (.53,y) is on the unit circle in quadrant 1, what is the value of y?
Unit circle equation:
x^2 + y^2 = 1
Plugging in x = 0.53, we get
(0.53)^2 + y^2 = 1
0.2809 + y^2 = 1
Subtract 0.2809 from each side:
y^2 = 0.7191
y = [B]0.848[/B]

If x varies directly with y and x = -3 when y = 12, what is the constant of variation?

If x varies directly with y and x = -3 when y = 12, what is the constant of variation?
Using our [URL='https://www.mathcelebrity.com/community/forums/calculator-requests.7/create-thread']variation calculator[/URL], we see the constant of variation (k) is:
k =[B] -1/4 or -0.25[/B]

If you paid $2.95 for 2.5 pounds of apples,what was the cost per pound?

If you paid $2.95 for 2.5 pounds of apples,what was the cost per pound?
Using our [URL='http://www.mathcelebrity.com/unit-cost-calculator.php?num=2poundbagfor2.95&pl=Calculate+Unit+Cost']unit cost calculator[/URL], we get $[B]1.48.[/B]

If you pay 9.70 dollars for 2.5 pounds of cheese, how much is it per pound?

This is a unit cost problem.
Use our [URL='http://www.mathcelebrity.com/unit-cost-calculator.php?num=2.5poundbagfor9.70&pl=Calculate+Unit+Cost']unit cost calculator[/URL] to find dollars per pound
[B]$2.88 / pound of cheese[/B]

Imagine a researcher posed a null hypothesis that in a certain community, the average energy expendi

Imagine a researcher posed a null hypothesis that in a certain community, the average energy expenditure should be 2,100 calories per day. He randomly sampled 100 people in that community. After he computed the t value by calculating a two-tailed t-statistic, he found that the probability value was 0.10. Thus, he concluded:
a. The average energy expenditure was bigger than 2,100 calories per day
b. The average energy expenditure was smaller than 2,100 calories per day
c. He could not reject the null hypothesis that the average energy expenditure was 2,100 calories per day
d. The average energy expenditure was either more than 2,100 calories per day or less than 2,100 calories per day
[B]c. He could not reject the null hypothesis that the average energy expenditure was 2,100 calories per day[/B]
[I]p-value is higher than 0.05[/I]

International Unit Conversions

Free International Unit Conversions Calculator - This calculator converts between the following weight measurements:

* International Units (IU)

* mcg

* mg

* International Units (IU)

* mcg

* mg

it costs $75.00 for a service call from shearin heating and air conditioning company. the charge for

it costs $75.00 for a service call from shearin heating and air conditioning company. the charge for labor is $60.00 . how many full hours can they work on my air conditioning unit and still stay within my budget of $300.00 for repairs and service?
Our Cost Function is C(h), where h is the number of labor hours. We have:
C(h) = Variable Cost * Hours + Fixed Cost
C(h) = 60h + 75
Set C(h) = $300
60h + 75 = 300
[URL='https://www.mathcelebrity.com/1unk.php?num=60h%2B75%3D300&pl=Solve']Running this problem in the search engine[/URL], we get [B]h = 3.75[/B].

It takes 3 city snowplows 14 hours to clear 500 miles of road. If the city wants the 500 miles of ro

It takes 3 city snowplows 14 hours to clear 500 miles of road. If the city wants the 500 miles of road to be cleared in 6 hours, how many additional snowplows must they buy?
Set up unit rate per plow:
14 hours * 3 plows = 42 hours for one plow to clear 500 miles of road
Calculate the amount of plows we need:
42 hours / 6 hours = 7 plows
Additional plows = New plows - original plows:
Additional plows = 7 - 3
Additional plows = [B]4[/B]

It takes a crew of 4 painters 12 hours one house. If they wanted to paint the house in 8 hours, how

It takes a crew of 4 painters 12 hours one house. If they wanted to paint the house in 8 hours, how many additional painters must they hire?
It takes one painter 4 * 12 hours = 48 hours to paint the house.
Now we calculate the unit rate:
48 hours / 8 hours = 6 painters
6 painters - 4 original painters = [B]2 additional painters[/B]

Jelaskan secara tepat, memperagakan balok garis bilangan untuk menjelaskan bentuk operasi (-6)-(-8)

Jelaskan secara tepat, memperagakan balok garis bilangan untuk menjelaskan bentuk operasi (-6)-(-8)
Tolak negatif adalah positif. Oleh itu, kami mempunyai:
-6 + 8 = [B]2
Pada garis nombor, kita mulai pada -6 dan beralih ke kanan 8 unit menjadi 2[/B]

Jessica has 16 pairs of shoes. She buys 2 additional pair of shoes every month. What is the slope in

Jessica has 16 pairs of shoes. She buys 2 additional pair of shoes every month. What is the slope in this situation?
Set up a graph where months is on the x-axis and number of shoes Jessica owns is on the y-axis.
[LIST=1]
[*]Month 1 = (1, 18)
[*]Month 2 = (2, 20)
[*]Month 3 = (3, 22)
[*]Month 4 = (4, 24)
[/LIST]
You can see for every 1 unit move in x, we get a 2 unit move in y.
Pick any of these 2 points, and [URL='https://www.mathcelebrity.com/slope.php?xone=3&yone=22&slope=+2%2F5&xtwo=4&ytwo=24&pl=You+entered+2+points']use our slope calculator[/URL] to get:
Slope = [B]2[/B]

Joaquin buys 3 dozen lightbulbs. After changing the lightbulbs in his house,he has 15 lightbulbs lef

Joaquin buys 3 dozen lightbulbs. After changing the lightbulbs in his house,he has 15 lightbulbs left. How many lightbulbs did he use?
[URL='https://www.mathcelebrity.com/quantcon.php?quant=3&pl=Calculate&type=dozen']Type 3 dozen into the search engine[/URL]. We get 36 units.
Now, if Joaquin has 15 lightbulbs left, we subtract 15 from 36: 36 - 15 = [B]21 lightbulbs used[/B]

John need 250 hours of community service. He volunteers 2 days a week for 4 hours. How long will it

John need 250 hours of community service. He volunteers 2 days a week for 4 hours. How long will it take John to reach 250 hours?
Each week, John serves 2 days * 4 hours per day = 8 hours.
We divide 250/8 to get [B]31.25 weeks[/B].

Kartek bought 86 pizzas for a school party. If there are 516 people at his school, how much pizza sh

Kartek bought 86 pizzas for a school party. If there are 516 people at his school, how much pizza should each person get?
Setup unit slices:
[URL='https://www.mathcelebrity.com/search.php?q=86%2F516']86 pizzas / 516 people[/URL] = [B]1/6 pizza per person[/B]

Lauren wrote a total of 6 pages over 2 hours. How many hours will Lauren have to spend writing this

Lauren wrote a total of 6 pages over 2 hours. How many hours will Lauren have to spend writing this week in order to have written a total of 9 pages? Solve using unit rates.
6 pages per 2 hours equals 6/2 = 3 pages per hour as a unit rate
Set up equation using h hours:
3h = 9
Divide each side by 3
[B]h = 3[/B]

Linda takes classes at both Westside Community College and Pinewood Community College. At Westside,

Linda takes classes at both Westside Community College and Pinewood Community College. At Westside, class fees are $98 per credit hour, and at Pinewood, class fees are $115 per credit hour. Linda is taking a combined total of 18 credit hours at the two schools. Suppose that she is taking w credit hours at Westside. Write an expression for the combined total dollar amount she paid for her class fees.
Let p be the number of credit hours at Pinewood. We have two equations:
[LIST]
[*]98w for Westside
[*]115p at Pinewood
[*]w + p = 18
[*]Total fees: [B]98w + 115p[/B]
[/LIST]

Lunch meat A is 10.00 for 2 lbs or meat B for 6.00 for 1lb

Lunch meat A is 10.00 for 2 lbs or meat B for 6.00 for 1lb
Determine unit cost:
Unit Cost A = 10/2 lbs = 5 per lb
Unit Cost B = 6/1lb = 6 per lb
[B]Unit Cost A is less, so that is the better buy.[/B]

Map Scale

Free Map Scale Calculator - Solves map scale problems based on unit measurements

Michelle can paint one car in 2 hours. It takes Tyler 3 hours to paint the same car while Colton tak

Michelle can paint one car in 2 hours. It takes Tyler 3 hours to paint the same car while Colton takes 6 hours to paint the car. If they all work together, how long will it take them to paint the car?
Setup unit rates:
[LIST]
[*]Michelle can paint 1/2 of the car in one hour
[*]Tyler can paint 1/3 of the car in one hour
[*]Colton can paint 1/6 of the car in one hour
[/LIST]
In one hour using a combined effort, they can paint:
1/2 + 1/3 + 1/6 = 6/6 = 1 car in [B]one hour[/B].

Number Property

Free Number Property Calculator - This calculator determines if an integer you entered has any of the following properties:

* Even Numbers or Odd Numbers (Parity Function or even-odd numbers)

* Evil Numbers or Odious Numbers

* Perfect Numbers, Abundant Numbers, or Deficient Numbers

* Triangular Numbers

* Prime Numbers or Composite Numbers

* Automorphic (Curious)

* Undulating Numbers

* Square Numbers

* Cube Numbers

* Palindrome Numbers

* Repunit Numbers

* Apocalyptic Power

* Pentagonal

* Tetrahedral (Pyramidal)

* Narcissistic (Plus Perfect)

* Catalan

* Repunit

* Even Numbers or Odd Numbers (Parity Function or even-odd numbers)

* Evil Numbers or Odious Numbers

* Perfect Numbers, Abundant Numbers, or Deficient Numbers

* Triangular Numbers

* Prime Numbers or Composite Numbers

* Automorphic (Curious)

* Undulating Numbers

* Square Numbers

* Cube Numbers

* Palindrome Numbers

* Repunit Numbers

* Apocalyptic Power

* Pentagonal

* Tetrahedral (Pyramidal)

* Narcissistic (Plus Perfect)

* Catalan

* Repunit

Potato chips were $29.26 for 7 bags.Brand B was $25.38 for 6 bags which is the better buy

Potato chips were $29.26 for 7 bags.Brand B was $25.38 for 6 bags which is the better buy.
Using our [URL='http://www.mathcelebrity.com/betterbuy.php?p1=29.26&p2=25.38&q1=7&q2=6&pl=Better+Buy']better buy calculator[/URL], we get:
[LIST]
[*]Potato Chips have a unit cost of $4.18
[*]Brand B has a unit cost of $4.23
[*]Since Potato Chips have a lower unit cost, [B]Potato Chips are the better buy[/B]
[/LIST]

Sergeant U has 360 rounds of ammunition to distribute to Lance Corporal (LCpl) F, Lance Corporal (LC

Sergeant U has 360 rounds of ammunition to distribute to Lance Corporal (LCpl) F, Lance Corporal (LCpl) M and Lance Corporal (LCpl) Z in the ratio 3:5:7. How many rounds did Lance Corporal (LCpl) M receive?
Our ratio denominator is:
3 + 5 + 7 = 15
Lance Corporal (LCpl) M gets 5:15 of the ammunition. [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F15&frac2=3%2F8&pl=Simplify']Using our fraction simplifier[/URL], we see that 5/15 = 1/3
So we take 360 rounds of ammunition times 1/3:
360/3 = [B]120[/B]

Shen buys a pack of 9 towels for $24.30. Find the unit price in dollars per towel.

Shen buys a pack of 9 towels for $24.30. Find the unit price in dollars per towel.
Unit Price = Total Price/Units
Unit Price = 24.30/9
Unit Price = [B]2.7[/B]

Soda cans are sold in a local store for 50 cents each. The factory has $900 in fixed costs plus 25 c

Soda cans are sold in a local store for 50 cents each. The factory has $900 in fixed costs plus 25 cents of additional expense for each soda can made. Assuming all soda cans manufactured can be sold, find the break-even point.
Calculate the revenue function R(c) where s is the number of sodas sold:
R(s) = Sale Price * number of units sold
R(s) = 50s
Calculate the cost function C(s) where s is the number of sodas sold:
C(s) = Variable Cost * s + Fixed Cost
C(s) = 0.25s + 900
Our break-even point is found by setting R(s) = C(s):
0.25s + 900 = 50s
We [URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%2B900%3D50s&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]18.09[/B]

Solve for x

[IMG]https://mathcelebrity.com/community/data/attachments/0/supp-angles.jpg[/IMG]
The angle with measurements of 148 degrees lies on a straight line, which means it's supplementanry angle is:
180 - 148 = 32
Since the angle of 2x - 16 and 32 lie on a straight line, their angle sum equals 180:
2x + 16 + 32 = 180
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B16%2B32%3D180&pl=Solve']type it in our math engine [/URL]and we get:
x = [B]66[/B]

the absolute value of a number is its _____ from 0

the absolute value of a number is its _____ from 0
The answer is [B]distance[/B].
As an example: 2 and -2 are 2 units away from 0.

The base of a triangle with a height of 7 units is represented by the formula b=2/7A. The base of th

The 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 cost of tuition at Johnson Community College is $160 per credit hour. Each student also has to p

The cost of tuition at Johnson Community College is $160 per credit hour. Each student also has to pay $50 in fees. Model the cost, C, for x credit hours taken.
Set up cost equation, where h is the number of credit hours:
[B]C = 50 + 160h[/B]

The cost of X pounds of cheese or $6.75 a pound

The cost of X pounds of cheese or $6.75 a pound
Total Cost = Unit Cost * units
Total Cost = [B]$6.75 * x[/B]

The difference between two positive numbers is 5 and the square of their sum is 169

The difference between two positive numbers is 5 and the square of their sum is 169.
Let the two positive numbers be a and b. We have the following equations:
[LIST=1]
[*]a - b = 5
[*](a + b)^2 = 169
[*]Rearrange (1) by adding b to each side. We have a = b + 5
[/LIST]
Now substitute (3) into (2):
(b + 5 + b)^2 = 169
(2b + 5)^2 = 169
[URL='https://www.mathcelebrity.com/community/forums/calculator-requests.7/create-thread']Run (2b + 5)^2 through our search engine[/URL], and you get:
4b^2 + 20b + 25
Set this equal to 169 above:
4b^2 + 20b + 25 = 169
[URL='https://www.mathcelebrity.com/quadratic.php?num=4b%5E2%2B20b%2B25%3D169&pl=Solve+Quadratic+Equation&hintnum=+0']Run that quadratic equation in our search engine[/URL], and you get:
b = (-9, 4)
But the problem asks for [I]positive[/I] numbers. So [B]b = 4[/B] is one of our solutions.
Substitute b = 4 into equation (1) above, and we get:
a - [I]b[/I] = 5
[URL='https://www.mathcelebrity.com/1unk.php?num=a-4%3D5&pl=Solve']a - 4 = 5[/URL]
[B]a = 9
[/B]
Therefore, we have [B](a, b) = (9, 4)[/B]

The graph shows the average length (in inches) of a newborn baby over the course of its first 15 mon

The graph shows the average length (in inches) of a newborn baby over the course of its first 15 months. Interpret the RATE OF CHANGE of the graph.
[IMG]http://www.mathcelebrity.com/community/data/attachments/0/rate-of-change-wp.jpg[/IMG]
Looking at our graph, we have a straight line. For straight lines, rate of change [U][I]equals[/I][/U] slope.
Looking at a few points, we have:
(0, 20), (12, 30)
Using our [URL='https://www.mathcelebrity.com/slope.php?xone=0&yone=20&slope=+2%2F5&xtwo=12&ytwo=30&pl=You+entered+2+points']slope calculator for these 2 points[/URL], we get a slope (rate of change) of:
[B]5/6[/B]

The monthly earnings of a group of business students are are normally distributed with a standard de

[URL]http://mathcelebrity.com/community/threads/standard-deviation-of-545-dollars-find-the-sample-size-needed-to-have-a-confidence-level-of-95-and.450/[/URL]

The sum of the digits of a 2 digit number is 10. The value of the number is four more than 15 times

The 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 the digits of a certain two-digit number is 16. Reversing its digits increases the number

The sum of the digits of a certain two-digit number is 16. Reversing its digits increases the number by 18. What is the number?
Let x and (16-x) represent the original ten and units digits respectively
Reversing its digits increases the number by 18
Set up the relational equation
[10x + (16-x)] + 18 = 10(16 - x) + x
Solving for x
9x + 34 = 160 - 9x
Combine like terms
18x = 126
Divide each side of the equation by 18
18x/18 = 126/18
x = 7
So 16 - x = 16 - 7 = 9
The first number is 79, the other number is 97. and 97 - 79 = 18 so we match up.
The number in our answer is [B]79[/B]

The total cost of 100 dresses is $1,500.00. The mark-up is estimated at 20% of the unit cost, the pr

The total cost of 100 dresses is $1,500.00. The mark-up is estimated at 20% of the unit cost, the price of a single dress using the cost-plus method will be
The phrase [I]unit cost[/I] means price per one unit.
[U]Unit cost for one dress is:[/U]
Price of dresses / Number of dresses
1500/100
15
Each dress cost $15 which is the unit cost
[U]Cost plus method:[/U]
Cost plus price = Unit price + Unit price * markup
Cost plus price = 15 + 15 * 20%
Cost plus price = 15 + 3
Cost plus price = [B]$18
[MEDIA=youtube]H9rOp592y5s[/MEDIA][/B]

The total cost of producing x units for which the fixed cost are $2500 and the cost per unit $20

The total cost of producing x units for which the fixed cost are $2500 and the cost per unit $20
Total Cost = Cost per Unit * Units + Fixed Cost
Total Cost = [B]20x + 2500[/B]

The total cost of producing x units for which the fixed costs are $2900 and the cost per unit is $25

The total cost of producing x units for which the fixed costs are $2900 and the cost per unit is $25
[U]Set up the cost function:[/U]
Cost function = Fixed Cost + Variable Cost per Unit * Number of Units
[U]Plug in Fixed Cost = 2900 and Cost per Unit = $25[/U]
[B]C(x) = 2900 + 25x
[MEDIA=youtube]77PiD-VADjM[/MEDIA][/B]

The United States Department of Agriculture reports that 18% of Americans are now on food stamps. If

The United States Department of Agriculture reports that 18% of Americans are now on food stamps. If there are 250,000,000 Americans, how many are on food stamps?
Since 18% is 0.18, we have:
250,000 * 0.18 = 45,000

Time Conversions

Free Time Conversions Calculator - Converts units of time between:

* nanoseconds

* microseconds

* milliseconds

* centiseconds

* kiloseconds

* seconds

* minutes

* hours

* days

* weeks

* fortnights

* months

* quarters

* years

* decades

* centurys

* milleniums

converting minutes to hours

* nanoseconds

* microseconds

* milliseconds

* centiseconds

* kiloseconds

* seconds

* minutes

* hours

* days

* weeks

* fortnights

* months

* quarters

* years

* decades

* centurys

* milleniums

converting minutes to hours

Todd bought 5 ice cream sandwiches for $3.75. Bryce bought one ice cream sandwich for $1.00. Who got

Todd bought 5 ice cream sandwiches for $3.75. Bryce bought one ice cream sandwich for $1.00. Who got the better deal?
Todd's unit cost is found by:
Todd's Unit Cost = Total Price / Total Ice Cream Sandwiches
Todd's Unit Cost = $3.75/5
Todd's Unit Cost = $0.75
Bryce's unit cost is $1.00 per ice cream sandwich, so [B]Todd got the better deal.[/B]

Trade Cost

Free Trade Cost Calculator - Calculates the saved hours under the electrician/carpenter model of specializing in jobs as well as opportunity cost.

Trig Measurement

Free 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

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

Two Step equation word problems.

[URL]http://www.mathcelebrity.com/community/threads/maria-bought-7-boxes-a-week-later-half-of-all-her-boxes-were-destroyed-in-a-fire-there-are-now-onl.348/[/URL]

Unit Circle

Free Unit Circle Calculator - Determines if coordinates for a unit circle are valid, or calculates a variable for unit circle coordinates

Unit Conversions

Free Unit Conversions Calculator - Converts between a unit, pair, half-dozen, dozen, bakers dozen, and gross.

Unit Cost

Free Unit Cost Calculator - Calculates the unit cost based on a price and a quantity

Unit Cost Calculator

I just created a new [URL='http://www.mathcelebrity.com/unit-cost-calculator.php']unit cost calculator[/URL]. As more searches come in, I'll add more shortcuts.
First type of shortcut:
3 pound bag for $11.25

Unit Fraction

Free Unit Fraction Calculator - Determines the unit fraction for a fraction.

Unit Savings

Free Unit Savings Calculator - A discount and savings word problem using 2 people and full prices versus discount prices.

Units of Output (Service Output) Depreciation

Free 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)

Vectors

Free 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, proj_{B}A and and the vector component of A orthogonal to B → A - proj_{B}A

Also calculates the horizontal component and vertical component of a 2-D vector.

* 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, proj

Also calculates the horizontal component and vertical component of a 2-D vector.

What is a Unit Circle

Free What is a Unit Circle Calculator - This lesson walks you through what a unit circle is and how to use it

What is the correct translation of; 8 increased by a number is 10?

What is the correct translation of; 8 increased by a number is 10?
We [URL='https://www.mathcelebrity.com/community/forums/calculator-requests.7/create-thread']type in [I]8 increased by a number is 10[/I] into our search engine[/URL] and we get:
[B]8 + a = 10[/B]

When the drain is closed, a swimming pool can be filled in 4 hours. When the drain is opened, it tak

When the drain is closed, a swimming pool can be filled in 4 hours. When the drain is opened, it takes 5 hours to empty the pool. The pool is being filled, but the drain was accidentally left open. How long until the pool is completely filled?
Set up unit fill rates per hour:
[LIST]
[*]1/4 of the pool is filled each hour
[*]1/5 of the pool is drained away each hour
[/LIST]
The amount left over after an hour of filling minus draining is:
[URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F4&frac2=1%2F5&pl=Subtract']1/4 - 1/5[/URL] = 1/20
Therefore, it take [B]20 hours to fill the pool[/B]

which is a better deal, 8 pens for $6.16 or 7 pens for $5.46

which is a better deal, 8 pens for $6.16 or 7 pens for $5.46
Calculate unit cost for each deal:
[LIST=1]
[*]6.16/8 = 0.77 per pen
[*]5.46/7 = 0.78 per pen
[/LIST]
[B]So deal #1, $6.16 for 8 pens is the better deal [/B]since each pen costs less than the other deal

which number is the same distance from 0 on the number line as 4

which number is the same distance from 0 on the number line as 4
We use absolute value for distance.
Since 4 is 4 units right of 0 on the number line, we can also move 4 units left of 0 on the number line and we land on [B]-4[/B]

Work Word Problems

Free 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.

You are baking muffins for your class. There are 17 total students in your class and you have baked

You 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 baking muffins for your class. There are 17 total students in your class and you have baked

You 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.
[U]Calculate total muffins:[/U]
Total muffins = 2 muffins per student * 17 students
Total muffins = 34
[U]Set up the equation using x for muffins:[/U]
[B]x + 5 = 34
[/B]
[U]To Solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B5%3D34&pl=Solve']type it in our search engine[/URL] and we get:[/U]
x = [B]29
[/B]

You have saved $50 over the last two weeks and decide to treat yourself by buying some new clothes.

You have saved $50 over the last two weeks and decide to treat yourself by buying some new clothes. You go to the store and find two shirts and three pairs of jeans you like. The two shirts are buy-one-get-one half off, at $22.35 each. The three pairs of jeans are buy-two-get-one-free, at $23.70.
Tax Rate for Harmonized Sales Tax is 13%
a. What would be the total for the two shirts (don’t forget to include taxes)?
b. What would be the total for the three pairs of jeans (don’t forget to include taxes)?
c. Which would you buy and why?
a. Half of 22.35 is 11.18
So two shirts cost:
22.35 + 11.18 = 33.53
Cost with Tax of 13% is:
33.53 * 1.13 = [B]37.89
[/B]
b. Three pairs of jeans are calculated by cost of 1 pair times 2 jeans and you get the third one free:
23.70 * 2 = 47.40
Cost with Tax of 13% is:
47.40 * 1.13 = [B]53.56
[/B]
c. Calculate unit cost, which is cost per item
Unit cost of Shirts = 37.89 / 2 = [B]18.95[/B]
Unit cost of Jeans = 53.56 / 3 = [B]17.85
Buy the jeans since they have a lower unit cost[/B]

You pay 510.00 to rent a storage unit for 3 months the total cost includes an initial deposit plus a

You pay 510.00 to rent a storage unit for 3 months the total cost includes an initial deposit plus a monthly fee of 160.00. Write and equation that represents your total cost Y in dollars after X months.
Set up the cost function Y where x is the number of months you rent
[B]Y = 160x + 510[/B]

you start at a point on the number line and move 4 units left. If you are now at 10, then what was y

you start at a point on the number line and move 4 units left. If you are now at 10, then what was your original point?
Work backwards. If we're at 10, and we moved left, this means we add 4 to get back to our starting point:
10 + 4 = [B]14[/B]

You work for a remote manufacturing plant and have been asked to provide some data about the cost of

You work for a remote manufacturing plant and have been asked to provide some data about the cost of specific amounts of remote each remote, r, costs $3 to make, in addition to $2000 for labor. Write an expression to represent the total cost of manufacturing a remote. Then, use the expression to answer the following question. What is the cost of producing 2000 remote controls?
We've got 2 questions here.
Question 1: We want the cost function C(r) where r is the number of remotes:
C(r) = Variable Cost per unit * r units + Fixed Cost (labor)
[B]C(r) = 3r + 2000
[/B]
Question 2: What is the cost of producing 2000 remote controls.
In this case, r = 2000, so we want C(2000)
C(2000) = 3(2000) + 2000
C(2000) = 6000 + 2000
C(2000) = [B]$8000[/B]

Youre setting sales goals for next month. You base your goals on previous average sales. The actual

Youre setting sales goals for next month. You base your goals on previous average sales. The actual sales for the same month for the last four years have been 24 units, 30 units, 23 units, and 27 units. What is the average number of units you can expect to sell next month?
Find the average sales for the last four years:
Average Sales = Total Sales / 4
Average Sales = (24 + 30 + 23 + 27) / 4
Average Sales = 104 / 4
Average Sales = [B]26 units[/B]