addition - math operation involving the sum of elements

3timesanumberdecreasedby3

A necklace chain costs $15. Beads cost $2.50 each. You spend a total of $30 on a necklace and beads before tax. How many beads did you buy in addition to the necklace?
Let the number of beads be b. We're given the following equation:
2.5b + 15 = 30
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.5b%2B15%3D30&pl=Solve']type this equation into our search engine[/URL] and we get:
b = [B]6[/B]

A $480 TV was put on sale for 30% off. It didn't sell, so the price was lowered an additional percen

A $480 TV was put on sale for 30% off. It didn't sell, so the price was lowered an additional percent off the sale price, making the new sale price $285.60. What was the second percent discount that was given?
Let the second discount be d. We're given:
480 * (1 - 0.3)(1 - d) = 285.60
480(0.7)(1 - d) = 285.60
336(1 - d) = 285.60
336 - 336d = 285.60
[URL='https://www.mathcelebrity.com/1unk.php?num=336-336d%3D285.60&pl=Solve']Type this equation into our search engine[/URL] to solve for d and we get:
d = [B]0.15 or 15%[/B]

A bookstore was selling books for 50% off. A shelf in the store had a sign that said "Books on this

A bookstore was selling books for 50% off. A shelf in the store had a sign that said "Books on this shelf take an additional 25% off."
Leta picked out books from the discount shelf that had a regular price of $100. How much did Leta pay for the discounted books?
100 with 50% discount is $40
$50 with a 25% discount is $12.50 off
$50 - $12.50 = [B]$37.50[/B]

A cab company charges $5 per cab ride, plus an additional $1 per mile driven , How long is a cab rid

A cab company charges $5 per cab ride, plus an additional $1 per mile driven , How long is a cab ride that costs $13?
Let the number of miles driven be m. Our cost function C(m) is:
C(m) = Cost per mile * m + cab cost
C(m) = 1m + 5
The problem asks for m when C(m) = 13:
1m + 5 = 13
To solve this equation for m, [URL='https://www.mathcelebrity.com/1unk.php?num=1m%2B5%3D13&pl=Solve']we type it in our search engine[/URL] and we get:
m = [B]8[/B]

A cab company charges $5 per cab ride, plus an additional $3 per mile driven. How long is a cab ride

A cab company charges $5 per cab ride, plus an additional $3 per mile driven. How long is a cab ride that costs $17?
Let m be the number of miles driven. We setup the cost equation C(m):
C(m) = Cost per mile driven * miles driven + ride cost
C(m) = 3m + 5
The questions asks for m when C(m) is 17:
3m + 5 = 17
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=3m%2B5%3D17&pl=Solve']type it in our search engine[/URL] and we get:
m = [B]4[/B]

A carpet cleaner charges $75 to clean the first 180 sq ft of carpet. There is an additional charge

A carpet cleaner charges $75 to clean the first 180 sq ft of carpet. There is an additional charge of 25˘ per square foot for any footage that exceeds 180 sq ft and $1.30 per step for any carpeting on a staircase. A customers cleaning bill was $253.95. This included the cleaning of a staircase with 14 steps. In addition to the staircase, how many square feet of carpet did the customer have cleaned?
Calculate the cost of the staircase cleaning.
Staircase cost = $1.30 * steps
Staircase cost = $1.30 * 14
Staircase cost = $18.20
Subtract this from the cost of the total cleaning bill of $253.95. We do this to isolate the cost of the carpet.
Carpet cost = $253.95 - $18.20
Carpet cost = $235.75
Now, the remaining carpet cost can be written as:
75 + $0.25(s - 180) = $235.75 <-- were s is the total square foot of carpet cleaned
Multiply through and simplify:
75 + 0.25s - 45 = $235.75
Combine like terms:
0.25s + 30 = 235.75
[URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%2B30%3D235.75&pl=Solve']Type this equation into our search engine[/URL] to solve for s, and we get:
s = [B]823[/B]

A cell phone plan charges $1.25 for the first 400 minutes and $0.25 for each additional minute, x. W

A cell phone plan charges $1.25 for the first 400 minutes and $0.25 for each additional minute, x. Which represents the cost of the cell phone plan?
Let C(x) be the cost function where x is the number of minutes we have:
[B]C(x) = 1.25(min(400, x)) + 0.25(Max(0, 400 - x))[/B]

A cell phone plan costs $20 a month and includes 200 free minutes. Each additional minute costs 5 ce

A cell phone plan costs $20 a month and includes 200 free minutes. Each additional minute costs 5 cents. If you use your cell phone for at least 200 minutes a month, write a function C(x) that represents the total cost per x minutes.
We add the flat rate per month to 5% of the number of minutes [U]over[/U] 200:
[B]C(x) = 20 + 0.05(x - 200)[/B]

A cellular phone company charges a $49.99 monthly fee for 600 free minutes. Each additional minute c

A cellular phone company charges a $49.99 monthly fee for 600 free minutes. Each additional minute cost $.35. This month you used 750 minutes. How much do you owe?
Calculate the excess minutes over the standard plan:
Excess Minutes = 750 - 600
Excess Minutes = 150
Calculate additional cost:
150 additional minutes * 0.35 per additional minutes = $52.50
Add this to the standard plan cost of $49.99
$52.50 + $49.99 = [B]$102.49[/B]

A cellular phone company charges a $49.99 monthly fee for 600 free minutes. Each additional minute c

A cellular phone company charges a $49.99 monthly fee for 600 free minutes. Each additional minute costs $.35. This month you used 750 minutes. How much do you owe
[U]Find the overage minutes:[/U]
Overage Minutes = Total Minutes - Free Minutes
Overage Minutes = 750 - 600
Overage Minutes = 150
[U]Calculate overage cost:[/U]
Overage Cost = Overage Minutes * Overage cost per minute
Overage Cost = 150 * 0.35
Overage Cost = $52.5
Calculate total cost (how much do you owe):
Total Cost = Monthly Fee + Overage Cost
Total Cost = $49.99 + $52.50
Total Cost = [B]$102.49[/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 family decides to rent a canoe for an entire day. The canoe rental rate is $50 for the first three

A family decides to rent a canoe for an entire day. The canoe rental rate is $50 for the first three hours and then 20$ for each additional hour. Suppose the family can spend $110 for the canoe rental. What is the maximum number of hours the family can rent the canoe?
IF we subtract the $50 for the first 3 hours, we get:
110 - 50 = 60 remaining
Each additional hour is 20, so the max number of hours we can rent the canoe is
$60/20 = 3 hours additional plus the original 3 hours is [B]6 hours[/B]

A football team gained 4 yards on a play,lost 8 on the next play ,then gained 2 yards on the third p

A football team gained 4 yards on a play,lost 8 on the next play ,then gained 2 yards on the third play write and addition expression
Gains are expressed with positives (+) and losses are expressed with negatives (-):
[LIST]
[*]Gained 4 years: +4
[*]Lost 8 on the next play: -8
[*]Gained 2 yards on the third play: +2
[/LIST]
Expression:
[B]+4 - 8 + 2 = -2[/B]

A house rental company charges a $700 for a week stay plus an additional $4 per night for a roll awa

A house rental company charges a $700 for a week stay plus an additional $4 per night for a roll away bed. Your family rents a house for a week and pays $756. How many roll away beds did they rent?
Roll Away Beds = (Total Rental Price - Weekly Charge)/Per night bed fee
Plugging in our numbers, we get:
Roll Away Beds = (756 - 700)/4
Roll Away Beds = 56/4
Roll Away Beds = [B]14[/B]

A necklace chain costs $15. Beads cost $2.75 each. You spend a total of $28.75 on a necklace and bea

A necklace chain costs $15. Beads cost $2.75 each. You spend a total of $28.75 on a necklace and beads before tax. How many beads did you buy in addition to the necklace?
[U]Calculate the amount left to spend on beads:[/U]
Bead Spend = Total Spend - Necklace Cost
Bead Spend = $28.75 - $15
Bead Spend = $13.75
[U]Calculate the number of beads you bought:[/U]
Beads Bought = Bead Spend / Cost Per Bead
Beads Bought = $13.75 / $2.75
Beads Bought = [B]$5[/B]

A phone company offers two monthly charge plans. In Plan A, there is no monthly fee, but the custome

A phone company offers two monthly charge plans. In Plan A, there is no monthly fee, but the customer pays 8 cents per minute of use. In Plan B, the customer pays a monthly fee of $1.50 and then an additional 7 cents per minute of use.
For what amounts of monthly phone use will Plan A cost more than Plan B?
Set up the cost equations for each plan. The cost equation for the phone plans is as follows:
Cost = Cost Per Minute * Minutes + Monthly Fee
Calculate the cost of Plan A:
Cost for A = 0.08m + 0. <-- Since there's no monthly fee
Calculate the cost of Plan B:
Cost for B = 0.07m + 1.50
The problem asks for what amounts of monthly phone use will Plan A be more than Plan B. So we set up an inequality:
0.08m > 0.07m + 1.50
[URL='https://www.mathcelebrity.com/1unk.php?num=0.08m%3E0.07m%2B1.50&pl=Solve']Typing this inequality into our search engine[/URL], we get:
[B]m > 150
This means Plan A costs more when you use more than 150 minutes per month.[/B]

A pretzel factory has daily fixed costs of $1100. In addition, it costs 70 cents to produce each bag

A pretzel factory has daily fixed costs of $1100. In addition, it costs 70 cents to produce each bag of pretzels. A bag of pretzels sells for $1.80.
[U]Build the cost function C(b) where b is the number of bags of pretzels:[/U]
C(b) = Cost per bag * b + Fixed Costs
C(b) = 0.70b + 1100
[U]Build the revenue function R(b) where b is the number of bags of pretzels:[/U]
R(b) = Sale price * b
R(b) = 1.80b
[U]Build the revenue function P(b) where b is the number of bags of pretzels:[/U]
P(b) = Revenue - Cost
P(b) = R(b) - C(b)
P(b) = 1.80b - (0.70b + 1100)
P(b) = 1.80b = 0.70b - 1100
P(b) = 1.10b - 1100

A shipping service charges $0.43 for the first ounce and $0.29 for each additional ounce of package

A shipping service charges $0.43 for the first ounce and $0.29 for each additional ounce of package weight. Write an equation to represent the price P of shipping a package that weighs x ounces, for any whole number of ounces greater than or equal to 1.
Set up the price function P(x)
[B]P(x) = 0.43 + 0.29(x - 1)[/B]

A store sells books for 50% off on Sundays. The store advertises that on Easter Sunday the store tak

A store sells books for 50% off on Sundays. The store advertises that on Easter Sunday the store takes an additional 25% off. What would a pile of books cost on Easter Sunday that normally sell for $100 on a Thursday?
50% off means we'd pay 100% - 50% = 50%
An additional 25% off means we'd pay 100% - 25% = 75%
Build this percentage paid stack below
100 * 50% * 75% = [B]37.50[/B]

A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to s

A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to spend less than $12 on a ride. Which inequality can be used to find the distance Samantha can travel?
Set up the travel cost equation where m is the number of miles:
C(m) = 0.8m + 1.50
If Samantha wants to spend less than 12 per ride, we have an inequality where C(m) < 12:
[B]0.8m + 1.50 < 12[/B]

A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to s

A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to spend less than $12 on a ride. Which inequality can be used to find the distance Samantha can travel?
[LIST]
[*]Each ride will cost 1.50 + 0.8x where x is the number of miles per trip.
[*]This expression must be less than 12.
[/LIST]
[U]Setup the inequality:[/U]
1.5 + 0.8x < 12
[U]Subtracting 1.5 from each side of the inequality[/U]
0.8x < 10.5
[U]Simplifying even more by dividing each side of the inequality by 0.8, we have:[/U]
[B]x < 13.125[/B]

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most $10 to

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most $10 to spend on the cab ride, how far could she travel?
Set up a cost function C(m), where m is the number of miles:
C(m) = Cost per mile * m + flat rate
C(m) = 0.65m + 1.75
The problem asks for m when C(m) = 10
0.65m + 1.75 = 10
[URL='https://www.mathcelebrity.com/1unk.php?num=0.65m%2B1.75%3D10&pl=Solve']Typing this equation into the search engine[/URL], we get:
m = [B]12.692 miles[/B]

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to spend on the cab ride, how far could she travel
Set up a cost function C(m), where m is the number of miles Erica can travel. We have:
C(m) = 0.65m + 1.75
If C(m) = 10, we have:
0.65m + 1.75 = 10
[URL='https://www.mathcelebrity.com/1unk.php?num=0.65m%2B1.75%3D10&pl=Solve']Typing this equation into our search engine[/URL], we get:
m = 12.69 miles
If the problem asks for complete miles, we round down to 12 miles.

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to spend on the cab ride, how far could she travel?
Set up the cost function C(m) where m is the number of miles:
C(m) = 0.65m + 1.75
If Erica has $10, then C(m) = 10, so we have:
0.65m + 1.75 = 10
[URL='https://www.mathcelebrity.com/1unk.php?num=0.65m%2B1.75%3D10&pl=Solve']Typing this equation into the search engine[/URL], we get
m = 12.69
if the answer asks for whole number, then we round down to m = 12

A taxi charges a flat rate of 1.75, plus an additional 0.65 per mile. If Erica has at most 10 to spe

A taxi charges a flat rate of 1.75, plus an additional 0.65 per mile. If Erica has at most 10 to spend on the cab ride, how far could she travel?
Setup an equation where x is the number of miles traveled:
0.65x + 1.75 = 10
Subtract 1.75 from each side:
0.65x = 8.25
Divide each side by 0.65
[B]x = 12.69 miles[/B]
If we do full miles, we round down to 12.

A tow truck charges a service fee of $50 and an additional fee of $1.75 per mile. What distance was

A tow truck charges a service fee of $50 and an additional fee of $1.75 per mile. What distance was Marcos car towed if he received a bill for $71
Set up a cost equation C(m) where m is the number of miles:
C(m) = Cost per mile * m + Service Fee
Plugging in the service fee of 50 and cost per mile of 1.75, we get:
C(m) = 1.75m + 50
The question asks for what m is C(m) = 71. So we set C(m) = 71 and solve for m:
1.75m + 50 = 71
Solve for [I]m[/I] in the equation 1.75m + 50 = 71
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 50 and 71. To do that, we subtract 50 from both sides
1.75m + 50 - 50 = 71 - 50
[SIZE=5][B]Step 2: Cancel 50 on the left side:[/B][/SIZE]
1.75m = 21
[SIZE=5][B]Step 3: Divide each side of the equation by 1.75[/B][/SIZE]
1.75m/1.75 = 21/1.75
m = [B]12[/B]

A vertical line that passes through the point (3, -2). Identify TWO additional points on the line.

A vertical line that passes through the point (3, -2). Identify TWO additional points on the line.
A vertical line runs straight up, so the x-coordinate is always the same.
We use x = 3 and any y point:
(3, -1)
(3, 0)
(3, 1)

A yoga member ship costs $16 and additional $7 per class. Write a linear equation modeling the cost

A yoga member ship costs $16 and additional $7 per class. Write a linear equation modeling the cost of a yoga membership?
Set up the cost function M(c) for classes (c)
[B]M(c) = 16 + 7c[/B]

Aaron is staying at a hotel that charges $99.95 per night plus tax for a room. A tax of 8% is applie

Aaron is staying at a hotel that charges $99.95 per night plus tax for a room. A tax of 8% is applied to the room rate, and an additional onetime untaxed fee of $5.00 is charged by the hotel. Which of the following represents Aaron’s total charge, in dollars, for staying [I]x[/I] nights?
[LIST]
[*]The Room cost equals 99.95 times x where x is the number of rooms
[*]We express an 8% tax by multiplying the room cost by 1.08
[*]Finally, we add on $5, which is [I]untaxed[/I]
[/LIST]
[I][/I]
Take this in pieces:
Room Cost: 99.95x
Tax on Room 1.08(99.95x)
Add on $5 which is untaxed: [B]1.08(99.95x) + 5[/B]

Addition and Multiplication Multiples

Shows all addition and multiplication multiples up to 20 for a positive integer

Addition and Multiplication Tables (Times Tables)

Shows the color coded addition or multiplication table entries and answer for any 2 numbers 1-15.

Addition Equality Property

Demonstrates the Addition Equality Property
Numerical Properties

Addition of 3 or more numbers

This calculator performs addition with carrying and an addition grid for 3 or more numbers.

Addition Property Of Inequality

Demonstrates the Addition Property Of Inequality.
Numerical Properties

Algebra Master (Polynomials)

Given 2 polynomials this does the following:

1) Polynomial Addition

2) Polynomial Subtraction

Also generates binomial theorem expansions and polynomial expansions with or without an outside constant multiplier.

1) Polynomial Addition

2) Polynomial Subtraction

Also generates binomial theorem expansions and polynomial expansions with or without an outside constant multiplier.

Allan built an additional room onto his house. The length of the room is 3 times the width. The peri

Allan built an additional room onto his house. The length of the room is 3 times the width. The perimeter of the room is 60 feet. What is the length of the room
A room is a rectangle. We know the perimeter of a rectangle is:
P = 2l + 2w
We're given two equations:
[LIST=1]
[*]l = 3w
[*]P = 60
[/LIST]
Plug (1) and (2) into our rectangle perimeter formula:
2(3w) + w = 60
6w + w = 60
[URL='https://www.mathcelebrity.com/1unk.php?num=6w%2Bw%3D60&pl=Solve']Type this equation into our search engine[/URL] to solve for w:
w = 8.5714
Now plug w = 8.5714 into equation 1 to solve for l:
l = 3(8.5714)
l = [B]25.7142[/B]

Amy and ryan operate a car dealing and repair service. For a car detailing (full wash outside and in

Amy and ryan operate a car dealing and repair service. For a car detailing (full wash outside and inside. Amy charges 40$ and Ryan charges 50$ . In addition they charge a hourly rate. Amy charges $35/h and ryan charges $30/h. How many hours does amy and ryan have to work to make the same amount of money?
Set up the cost functions C(h) where h is the number of hours.
[U]Amy:[/U]
C(h) = 35h + 40
[U]Ryan:[/U]
C(h) = 30h + 50
To make the same amount of money, we set both C(h) functions equal to each other:
35h + 40 = 30h + 50
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=35h%2B40%3D30h%2B50&pl=Solve']type this equation into our search engine[/URL] and we get:
h = [B]2[/B]

Associative Property

Demonstrates the associative property using 3 numbers. Covers the Associative Property of Addition and Associative Property of Multiplication. Also known as the Associative Law of Addition and Associative Law of Multiplication
Numerical Properties

Balancing Equations

Given 4 numbers, this will use the four operations: addition, subtraction, multiplication, or division to balance the equations if possible.

Basic m x n Matrix Operations

Given 2 matrices |A| and |B|, this performs the following basic matrix operations

* Matrix Addition |A| + |B|

* Matrix Subtraction |A| - |B|

* Matrix Multiplication |A| x |B|

* Scalar multiplication rA where r is a constant.

* Matrix Addition |A| + |B|

* Matrix Subtraction |A| - |B|

* Matrix Multiplication |A| x |B|

* Scalar multiplication rA where r is a constant.

Basic Math Operations

Given 2 numbers, this performs the following arithmetic operations:

* Addition (Adding) (+)

* Subtraction (Subtracting) (-)

* Multiplication (Multiplying) (x)

* Long division (Dividing) with a remainder (÷)

* Long division to decimal places (÷)

* Partial Sums (Shortcut Sums)

* Short Division

* Duplication and Mediation

* Addition (Adding) (+)

* Subtraction (Subtracting) (-)

* Multiplication (Multiplying) (x)

* Long division (Dividing) with a remainder (÷)

* Long division to decimal places (÷)

* Partial Sums (Shortcut Sums)

* Short Division

* Duplication and Mediation

Bawi solves a problem that has an answer of x = -4. He first added 7 to both sides of the equal sign

Bawi solves a problem that has an answer of x = -4. He first added 7 to both sides of the equal sign, then divided by 3. What was the original equation
[LIST=1]
[*]If we added 7 to both sides, that means we had a minus 7 (-7) to start with as a constant. Since subtraction undoes addition.
[*]If we divided by 3, this means we multiplied x by 3 to begin with. Since division undoes multiplication
[/LIST]
So we have the start equation:
3x - 7
If the answer was x = -4, then we plug this in to get our number on the right side of the equation:
3(-4) - 7
-12 - 7
-19
This means our original equation was:
[B]3x - 7 = -19[/B]
And if we want to solve this to prove our answer, we [URL='https://www.mathcelebrity.com/1unk.php?num=3x-7%3D-19&pl=Solve']type the equation into our search engine [/URL]and we get:
x = -4

Bike rental shop A charges $20 per kilometre travelled with no additional fee. Bike rental shop B ch

Bike rental shop A charges $20 per kilometre travelled with no additional fee. Bike rental shop B charges only $8 per kilometre travelled, but has a starting charge of $35. If Bob plans to travel 7km by bike, which rental shop should he choose for a better price
[U]Shop A Cost function C(k) where k is the number of kilometers used[/U]
C(k) = Cost per kilometer * k + Starting Charge
C(k) = 20k
With k = 7, we have:
C(7) = 20 * 7
C(7) = 140
[U]Shop B Cost function C(k) where k is the number of kilometers used[/U]
C(k) = Cost per kilometer * k + Starting Charge
C(k) = 8k + 35
With k = 7, we have:
C(7) = 8 * 7 + 35
C(7) = 56 + 35
C(7) = 91
Bog should choose [B]Shop B[/B] since they have the better price for 7km

Carl is taking a math test. There are 10 questions which take 30 seconds each; 15 questions which ta

Carl is taking a math test. There are 10 questions which take 30 seconds each; 15 questions which take 40 seconds each; and 12 questions which take 2 minutes each. Carl pauses for 5 seconds between questions. In addition, he sharpens his pencil twice, which takes 20 seconds each time. The test begins promptly at 10:00 am. When Carl hands in his completed test, what time is it?
[U]10 Questions:[/U]
[LIST]
[*]30 seconds each x 10 questions = 5 minutes
[*]10 pauses between questions x 5 seconds per question = 50 seconds
[/LIST]
[U]15 Questions[/U]
[LIST]
[*]40 seconds each x 15 questions = 600 seconds, or 10 minutes
[*]15 pauses between questions x 5 seconds per question = 75 seconds, or 1 minute, 15 seconds
[/LIST]
[U]12 Questions[/U]
[LIST]
[*]2 minutes x 12 questions = 24 minutes
[*]12 pauses x 5 seconds per question = 60 seconds, or 1 minute
[/LIST]
[U]2 Pencil Sharpenings[/U]
[LIST]
[*]2 pencil sharpening x 20 seconds each = 40 seconds
[/LIST]
[U]Total Time[/U]
5 minutes, 50 seconds
11 minutes, 15 seconds
25 minutes
40 seconds
41 minutes and 105 seconds
But 105 seconds is 1 minute, 45 seconds.
So we have 41 minutes, 45 seconds
Therefore, it's [B]10:41[/B]

Carly has already written 35 of a novel. She plans to write 12 additional pages per month until she

Carly has already written 35 of a novel. She plans to write 12 additional pages per month until she is finished. Write and solve a linear equation to find the total number of pages written at 5 months.
Let m be the number of months. We have the pages written function P(m) as:
P(m) = 12m + 35
The problem asks for P(5):
P(5) = 12(5) + 35
P(5) = 60 + 35
P(5) = [B]95[/B]

Carly has already written 35 pages of a novel. She plans to write 12 additional pages per month unti

Carly has already written 35 pages of a novel. She plans to write 12 additional pages per month until she is finished. Write and solve a linear equation to find the total number of pages written at 5 months.
Set up the equation where m is the number of months:
pages per month * m + pages written already
12m + 35
The problems asks for m = 5:
12(5) + 35
60 + 35
[B]95 pages[/B]

Cassidy is renting a bicycle on the boardwalk. The rental costs a flat fee of $10 plus an additional

Cassidy is renting a bicycle on the boardwalk. The rental costs a flat fee of $10 plus an additional $7 per hour. Cassidy paid $45 to rent a bicycle.
We set up the cost equation C(h) where h is the number of hours of rental:
C(h) = hourly rental rate * h + Flat Fee
C(h) = 7h + 10
We're told that Cassidy paid 45 to rent a bicycle, so we set C(h) = 45
7h + 10 = 45
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=7h%2B10%3D45&pl=Solve']type this equation into our math engine[/URL] and we get:
h = [B]5[/B]

Commutative Property

Demonstrates the commutative property of addition and the commutative property of multiplication using 3 numbers.
Numerical Properties

Complex Number Operations

Given two numbers in complex number notation, this calculator:

1) Adds (complex number addition), Subtracts (complex number subtraction), Multiplies (complex number multiplication), or Divides (complex number division) any 2 complex numbers in the form a + bi and c + di where i = √-1.

2) Determines the Square Root of a complex number denoted as √a + bi

3) Absolute Value of a Complex Number |a + bi|

4) Conjugate of a complex number a + bi

1) Adds (complex number addition), Subtracts (complex number subtraction), Multiplies (complex number multiplication), or Divides (complex number division) any 2 complex numbers in the form a + bi and c + di where i = √-1.

2) Determines the Square Root of a complex number denoted as √a + bi

3) Absolute Value of a Complex Number |a + bi|

4) Conjugate of a complex number a + bi

Computers R US was selling laptops that had 4GB of memory for $495. You can buy additional memory fo

Computers R US was selling laptops that had 4GB of memory for $495. You can buy additional memory for $97 per GB. If your grandfather gave you $980 to buy a laptop and additional memory, how much memory can you get?
Figure out remaining money total after buying the laptop
[LIST=1]
[*]4GB: 980 - 495 = 485
[*]485/97 = 5 GB
[*]4GB + 5GB = [B]9GB[/B]
[/LIST]

Counting on a Number Line

Shows addition or subtraction by moving left or right on a number line.

Eight workers dug 3/8 of a tunnel in 10 days. If they need to finish the remaining 5/8 of the tunnel

Eight workers dug 3/8 of a tunnel in 10 days. If they need to finish the remaining 5/8 of the tunnel in 3 & 1/3 days, how many more workers must they hire?
Eight workers * 10 days = 80 days for one worker
If 3/8 of a tunnel took 80 days for one worker, then each 1/8 of a tunnel takes a single worker:
80/3 = 26 & 2/3 days
Multiply by 5 for the remaining 5/8 and we get:
133 & 1/3
We need 133 & 1/3 / 3 & 1/3 = 40 workers needed
Additional workers = Workers Needed - Original Workers
Additional workers = 40 - 8
Additional workers = [B]32[/B]

Finite Field

Demonstrates the addition table and multiplication table for a finite field (Galois Field) of n denoted GF(n).

For her phone service, Maya pays a monthly fee of $27 , and she pays an additional $0.04 per minu

For her phone service, Maya pays a monthly fee of $27 , and she pays an additional $0.04 per minute of use. The least she has been charged in a month is $86.04 . What are the possible numbers of minutes she has used her phone in a month? Use m for the number of minutes, and solve your inequality for m .
Maya's cost function is C(m), where m is the number of minutes used.
C(m) = 0.04m + 27
We are given C(m) = $86.04. We want her cost function [I]less than or equal[/I] to this.
0.04m + 27 <= 86.04
[URL='https://www.mathcelebrity.com/1unk.php?num=0.04m%2B27%3C%3D86.04&pl=Solve']Type this inequality into our search engine[/URL], and we get [B]m <= 1476[/B].

Fractions and Mixed Numbers

Given (improper fractions, proper fraction, mixed numbers, or whole numbers), this performs the following operations:

* Addition (Adding)

* Subtraction (Subtracting)

* Positive Difference (Absolute Value of the Difference)

* Multiplication (Multiplying)

* Division (Dividing: complex fraction division is included)

* Compare Fractions

* Simplifying of proper and improper fractions as well as mixed numbers. Fractions will be reduced down as far as possible (Reducing Fractions).

* Reciprocal of a Fraction

* Find all fractions between two fractions

* reduce a fraction

* Addition (Adding)

* Subtraction (Subtracting)

* Positive Difference (Absolute Value of the Difference)

* Multiplication (Multiplying)

* Division (Dividing: complex fraction division is included)

* Compare Fractions

* Simplifying of proper and improper fractions as well as mixed numbers. Fractions will be reduced down as far as possible (Reducing Fractions).

* Reciprocal of a Fraction

* Find all fractions between two fractions

* reduce a fraction

Given:

Given:

Given: BC = EF
AC = EG
AB = 10
BC = 3
Prove FG = 10
[LIST]
[*]AC = AB + BC (Segment Addition Postulate)
[*]AB = 10, BC = 3 (Given)
[*]AC = 10 + 3 (Substitution Property of Equality)
[*]AC = 13 (Simplify)
[*]AC = EG, BC = EF (Given)
[*]EG = 13, EF = 3 (Segment Equivalence)
[*]EG = EF + FG (Segment Addition Postulate)
[*]13 = 3 + FG (Substitution Property of Equality)
[*]FG = 10 (Subtraction Property)
[/LIST]

Hans rented a truck for one day. There was a base fee of 16.95, and there was an additional charge o

Hans rented a truck for one day. There was a base fee of 16.95, and there was an additional charge of 76 cents for each mile driven. Hans had to pay 152.99 when he returned the truck. For how many miles did he drive the truck?
Set up the equation where x is the amount of miles he drove:
0.76x + 16.95 = 152.99
[URL='http://www.mathcelebrity.com/1unk.php?num=0.76x%2B16.95%3D152.99&pl=Solve']Plug this equation into our calculator[/URL]:
x = 179 miles

If Ef = 3x,Fg = 2x,and EG = 5

If Ef = 3x,Fg = 2x,and EG = 5
By segment addition, we have:
EF + FG = EG
3x + 2x = 5
To solve for x, we t[URL='https://www.mathcelebrity.com/1unk.php?num=3x%2B2x%3D5&pl=Solve']ype this equation into our math engine [/URL]and we get:
x = 1
So EF = 3(1) = [B]3[/B]
FG = 2(1) = [B]2[/B]

If EF = 7x , FG = 3x , and EG = 10 , what is EF?

If EF = 7x , FG = 3x , and EG = 10 , what is EF?
By segment addition:
EF + FG = EG
7x + 3x = 10
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=7x%2B3x%3D10&pl=Solve']type it in our search engine[/URL] and we get:
x = 1
Evaluating EF = 7x with x = 1, we get:
EF = 7 * 1
EF = [B]7[/B]

If EF = 9x - 17, FG = 17x - 14, and EG = 20x + 17, what is FG?

If EF = 9x - 17, FG = 17x - 14, and EG = 20x + 17, what is FG?
By segment addition, we know that:
EF + FG = EG
Substituting in our values for the 3 segments, we get:
9x - 17 + 17x - 14 = 20x + 17
Group like terms and simplify:
(9 + 17)x + (-17 - 14) = 20x - 17
26x - 31 = 20x - 17
Solve for [I]x[/I] in the equation 26x - 31 = 20x - 17
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 26x and 20x. To do that, we subtract 20x from both sides
26x - 31 - 20x = 20x - 17 - 20x
[SIZE=5][B]Step 2: Cancel 20x on the right side:[/B][/SIZE]
6x - 31 = -17
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants -31 and -17. To do that, we add 31 to both sides
6x - 31 + 31 = -17 + 31
[SIZE=5][B]Step 4: Cancel 31 on the left side:[/B][/SIZE]
6x = 14
[SIZE=5][B]Step 5: Divide each side of the equation by 6[/B][/SIZE]
6x/6 = 14/6
x = [B]2.3333333333333[/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 FG=11, GH=x-2, and FH=3x-11, what is FH

If FG=11, GH=x-2, and FH=3x-11, what is FH
By segment addition, we have:
FG + GH = FH
11 + x - 2 = 3x - 11
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=11%2Bx-2%3D3x-11&pl=Solve']type it in or math engine[/URL] and we get:
x = 10
FH = 3x - 11. So we substitute x = 10 into this:
FH = 3(10) - 11
FH = 30 - 11
FH = [B]19[/B]

If QR = 16, RS = 4x ? 17, and QS = x + 20, what is RS?

If QR = 16, RS = 4x ? 17, and QS = x + 20, what is RS?
From the segment addition rule, we have:
QR + RS = QS
Plugging our values in for each of these segments, we get:
16 + 4x - 17 = x + 20
To solve this equation for x, [URL='https://www.mathcelebrity.com/1unk.php?num=16%2B4x-17%3Dx%2B20&pl=Solve']we type it in our search engine[/URL] and we get:
x = 7
Take x = 7 and substitute it into RS:
RS = 4x - 17
RS = 4(7) - 17
RS = 28 - 17
RS = [B]11[/B]

if you buy 50 bales of hay at $3.56 each, and then buy an additional 234 bales at $3.33 each, how mu

if you buy 50 bales of hay at $3.56 each, and then buy an additional 234 bales at $3.33 each, how much do you pay for the entire lot of 284 bales?
Since cost = price * quantity, we have:
Total lot cost = price(1) of hay * bales(1) of hay + price(2) of hay * bales(2) of hay
Total lot cost = 3.56 * 50 + 3.33 * 24
Total lot cost = 178 + 79.92
Total lot cost = [B]257.92[/B]

In 2013, a local Dairy Queen had $502,000 in sales. In 2014, that same locations sales were up an ad

In 2013, a local Dairy Queen had $502,000 in sales. In 2014, that same locations sales were up an additional 43%. What was this Dairy Queens total sales in 2014?
2014 Sales = 2013 Sales * 1.43
2014 Sales = 502,000 * 1.43
2014 Sales = [B]717,860[/B]

Isabel will run less than 36 minutes today. So far, she has run 22 minutes. What are the possible nu

Isabel will run less than 36 minutes today. So far, she has run 22 minutes. What are the possible numbers of additional minutes she will run?
Set up our inequality. If she ran 22 minutes, we need to find an expression to find out the remaining minutes
x + 22 < 36
Subtract 22 from each side:
x < 14
Remember, she cannot run negative minutes, so our lower bound is 0, so we have:
[B]0 < x < 14
[/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]

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]

Joe is paid a 4% commission on all his sales in addition to a $500 per month salary. In May, his sal

Joe is paid a 4% commission on all his sales in addition to a $500 per month salary. In May, his sales were $100,235. How much money did he earn in May?
[U]The commission and salary formula is:[/U]
Earnings = Salary + Commission Percent * Sales
Plugging in our numbers with 4% as 0.04, we get:
Earnings = 500 + 0.04 * 100235
Earnings = 500 + 4009.40
Earnings = [B]4,509.40[/B]

Julia owes 18.20 for the month of November. Her plan costs 9.00 for the first 600 text messages and

Julia 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]

Julio has $150. Each week, he saves an additional $10. Write a function f(x) that models the total a

Julio has $150. Each week, he saves an additional $10. Write a function f(x) that models the total amount of money Julio has after x weeks
f(x) = Savings per week * number of weeks + starting amount
f(x) = [B]10x + 150[/B]

kira will spend less than 27 on gifts. so far, she has spent 12$. what are the possible additional a

kira will spend less than 27 on gifts. so far, she has spent 12$. what are the possible additional amounts she will spend?
The key word in this problem is [I]less than[/I]. So we know this is an inequality.
Let s be Kira's possible spend. We have:
s + 12 < 27
To solve for s in this inequality, we subtract 12 from each side:
s + 12 - 12 < 27 - 12
Cancel the 12's on the left side, and we get:
[B]s < 15
[/B]
[I]The summary here is Kira can spend anything up to [U]but not including[/U] 15[/I]

KL=4, and JK=9 Find JL

KL=4, and JK=9 Find JL
Using segment addition, we know that:
JL = JK + KL
JL = 9 + 4
JL = [B]13[/B]

Last month, a parking lot had 23 spaces in each of its rows. Recently, the lost was expanded, and 4

Last month, a parking lot had 23 spaces in each of its rows. Recently, the lost was expanded, and 4 spaces were added to each row. If the lot has 8 rows, how many spaces are there now?
23 spaces + 4 additional spaces = 27 spaces
27 spaces * 8 rows = [B]216 spaces[/B]

Logarithms

Using the formula Log a_{b} = e, this calculates the 3 pieces of a logarithm equation:

1) Base (b)

2) Exponent

3) Log Result

In addition, it converts

* Expand logarithmic expressions

1) Base (b)

2) Exponent

3) Log Result

In addition, it converts

* Expand logarithmic expressions

M is the midpoint of AB. Prove AB=2AM

M 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)

Maria called her sister long distance on Wednesday. The first 5 minutes cost $3, and each minute aft

Maria called her sister long distance on Wednesday. The first 5 minutes cost $3, and each minute after that cost $0.25. How much did it cost if they talked for 15 minutes?
First 5 minutes: $3
If they talked 15 minutes, the additional charge past 5 minutes is:
0.25 * (15 - 5)
0.25 * 10 minutes = $2.5
We add this to the first 5 minutes:
$3 + $2.5 = [B]$5.50[/B]

Maria is saving money to buy a bike that cost 133$. She has 42$ and will save an additional 7 each w

Maria is saving money to buy a bike that cost 133$. She has 42$ and will save an additional 7 each week.
Set up an equation with w as the number of weeks. We want to find w such that:
7w + 42 = 133
[URL='https://www.mathcelebrity.com/1unk.php?num=7w%2B42%3D133&pl=Solve']Typing this equation into our search engine[/URL], we get:
w = [B]13[/B]

Mary spent a total of $291.94 for a party. She spent $200.29 on food, plus an additional $30.55 for

Mary spent a total of $291.94 for a party. She spent $200.29 on food, plus an additional $30.55 for each hour of the party. How long was the party?
First, figure out the remaining cost after food:
291.94 -200.29 = 91.65
91.65 / 30.55 per hour = 3 hours

Mr. Crimmins bought 15 apples and 15 oranges. Each apple cost $1.00, each orange cost $1.50. How muc

Mr. Crimmins bought 15 apples and 15 oranges. Each apple cost $1.00, each orange cost $1.50. How much more did he spend on oranges than apples?
[U]Calculate apple spend:[/U]
Apple Spend = Apple Cost * Number of Apples
Apple Spend = $1.00 * 15
Apple Spend =[B] [/B]$15
[B][/B]
[U]Calculate apple spend:[/U]
Orange Spend = Orange Cost * Number of Oranges
Orange Spend = $1.50 * 15
Orange Spend = $22.50
[B][/B]
[U]Calculate the additional amount spent on oranges over apples:[/U]
Additional Orange Spend = Orange Spend - Apple Spend
Additional Orange Spend = $22.50 - $15.00
Additional Orange Spend = [B]$7.50[/B]

Name the property shown. 6 + 5 + 84 = 84 + 5 + 6

Name the property shown. 6 + 5 + 84 = 84 + 5 + 6
[B]
Commutative property of addition[/B]

Natalie made a deal with a farmer. She agreed to work for an entire year and in return, the farmer w

Natalie made a deal with a farmer. She agreed to work for an entire year and in return, the farmer would give her $10,200 plus a prize pig.
After working for 5 months, Natalie decided to quit. The farmer determined that 5 months of work was equal to $3375 plus the pig. How much money was the pig worth?
The value of a year's work is $10,200 plus a pig of unknown value. The farmer took away $6825 because Natalie worked 5 months. If Natalie worked 7 more months, she would have been paid the additional $6825.
6825/7 months work = $975 per month
A full year's work is $975 * 12 = $11,700
Pig value = Full years work - payout
Pig value = 11,700 - 10,200
Pig value = [B]1,500[/B]

Number Bonds

Adds or subtracts 2 numbers and using grouping by 10 or 100. Also called number bonds or addition facts. Multiplies two numbers using tape diagrams.

Oscar makes a large purchase at Home Depot and plans to rent one of its trucks to take his supplies

Oscar makes a large purchase at Home Depot and plans to rent one of its trucks to take his supplies home. The most he wants to spend on the truck is $56.00. If Home Depot charges $17.00 for the first 75 minutes and $5.00 for each additional 15 min, for how long can Oscar keep the truck and remain within his budget?
Set up the cost equation C(m) where m is the number of minutes for rental:
C(m) = 17 * min(m, 75) + max(0, 5(m - 75))
If Oscar uses the first 75 minutes, he spends $17. So he's left with:
$56 - $17 = $38
$38 / $5 = 7 Remainder 3
We remove the remainder 3, since it's not a full 15 minute block. So Oscar can rent the truck for:
7 * 15 minute blocks = [B]105 minutes[/B]

Percent Math

Simplifies expressions involving numbers and percents with respect to addition and subtraction

PQ=3.7 and PR=14.1 what is QR

PQ=3.7 and PR=14.1 what is QR
QR = PR - PQ by segment addition
QR = 14.1 - 3.7
QR = [B]10.4[/B]

Puzzle Master

A link to our friends: Puzzle Master has a large and unique collection of brain teasers; puzzles for sale. In addition they also carry chess,mechanical banks, puzzle books, magic trick books, boomerangs, etc.

Pythagorean Theorem

Figures out based on user entry the missing side or missing hypotenuse of a right triangle. In addition, the calculator shows the proof of the Pythagorean Theorem and then determines by numerical evaluation if the 2 sides and hypotenuse you entered are a right triangle using the Pythagorean Theorem

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]

Rafael is a software salesman. His base salary is $1900 , and he makes an additional $40 for every c

Rafael is a software salesman. His base salary is $1900 , and he makes an additional $40 for every copy of Math is Fun he sells. Let p represent his total pay (in dollars), and let c represent the number of copies of Math is Fun he sells. Write an equation relating to . Then use this equation to find his total pay if he sells 22 copies of Math is Fun.
We want a sales function p where c is the number of copies of Math is Fun
p = Price per sale * c + Base Salary
[B]p = 40c + 1900
[/B]
Now, we want to know Total pay if c = 22
p = 40(22) + 1900
p = 880 + 1900
p = [B]2780[/B]

Rita has spent $16 so far on gifts. The additional amount she will spend will be less than $14. What

Rita has spent $16 so far on gifts. The additional amount she will spend will be less than $14. What are the possible total amounts she will spend?
Rita will spend at least another cent on other gifts above the $16 she spent so far, but no more than $14. Also, the problem says less than 14. 16 + 14 is 30, so that is the top end of her spending.
Let's say her remaining spending is s. Set up the inequality for possible spending values.
[B]16 < s < 30[/B]

Ruth has already jarred 3 liters of jam and will jar an additional 1 liter of jam everyday. How much

Ruth has already jarred 3 liters of jam and will jar an additional 1 liter of jam everyday. How much jam did Ruth jar if she spent 7 days making jam?
7 days at 1 liter = 7 x 1 = 7.
Add that 7 to our original 3 and we have, 7 + 3 = 10 liters of jam.

She ordered 6 large pizzas. Luckily, she had a coupon for 3 off each pizza. If the bill came to 38.9

She ordered 6 large pizzas. Luckily, she had a coupon for 3 off each pizza. If the bill came to 38.94, what was the price for a large pizza?
[U]Determine additional amount the pizzas would have cost without the coupon[/U]
6 pizzas * 3 per pizza = 18
[U]Add 18 to our discount price of 38.94[/U]
Full price for 6 large pizzas = 38.94 + 18
Full price for 6 large pizzas = 56.94
Let x = full price per pizza before the discount. Set up our equation:
6x = 56.94
Divide each side by 6
[B]x = $9.49[/B]

Signed Integer Operations

This performs a string of signed integer operations, either all addition and subtraction, or all multiplication and division.

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]

Survival Rates

Given a set of times and survival population counts, the calculator will determine the following:

Survival Population l_{x}

Mortality Population d_{x}

Survival Probability p_{x}

Mortality Probability q_{x}

In addition, the calculator will determine the probability of survival from t_{x} to t_{x + n}

Survival Population l

Mortality Population d

Survival Probability p

Mortality Probability q

In addition, the calculator will determine the probability of survival from t

The charge to rent a trailer is $30 for up to 2 hours plus $9 per additional hour or portion of an

The charge to rent a trailer is $30 for up to 2 hours plus $9 per additional hour or portion of an hour. Find the cost to rent a trailer for 2.4 hours, 3 hours, and 8.5 hours.
Set up the cost function C(h), where h is the number of hours to rent the trailer. We have, for any hours greater than 2:
C(h) = 30 + 9(h - 2)
Simplified, we have:
C(h) = 9h - 18 + 30
C(h) = 9h + 12
The question asks for C(2.4), C(3), and C(8.5)
[U]Find C(2.4)[/U]
C(2.4) = 9(2.4) + 12
C(2.4) = 21.6 + 12
C(2.4) = [B]33.6
[/B]
[U]Find C(3)[/U]
C(3) = 9(3) + 12
C(3) = 27 + 12
C(2.4) = [B][B]39[/B][/B]
[U]Find C(8.5)[/U]
C(8.5) = 9(8.5) + 12
C(8.5) = 76.5 + 12
C(8.5) = [B]88.5[/B]

The cost for parking at a parking garage is 2.25 plus an additional 1.50 for each hour. What is the

The cost for parking at a parking garage is 2.25 plus an additional 1.50 for each hour. What is the total cost to park for 5 hours?
Set up our equation where C is cost and h is the number of hours used to park
C = 1.5h + 2.25
With h = 5, we have:
C = 1.5(5) + 2.25
C = 7.5 + 2.25
C = 9.75

The cost of a taxi ride is $1.2 for the first mile and $0.85 for each additional mile or part thereo

The cost of a taxi ride is $1.2 for the first mile and $0.85 for each additional mile or part thereof. Find the maximum distance we can ride if we have $20.75.
We set up the cost function C(m) where m is the number of miles:
C(m) = Cost per mile after first mile * m + Cost of first mile
C(m) = 0.8(m - 1) + 1.2
C(m) = 0.8m - 0.8 + 1.2
C(m) = 0.8m - 0.4
We want to know m when C(m) = 20.75
0.8m - 0.4 = 20.75
[URL='https://www.mathcelebrity.com/1unk.php?num=0.8m-0.4%3D20.75&pl=Solve']Typing this equation into our math engine[/URL], we get:
m = 26.4375
The maximum distance we can ride in full miles is [B]26 miles[/B]

The cost of renting a rototiller is $19.50 for the first hour and $7.95 for each additional hour. Ho

The cost of renting a rototiller is $19.50 for the first hour and $7.95 for each additional hour. How long can a person have the rototiller if the cost must be less than $95?
Setup the inequality:
$19.50 + $7.95x < $95
Subtract 19.50 from both sides:
7.95x < 75.50
Divide each side of the inequality by 7.95 to isolate x
x < 9.5
The next lowest integer is 9. So we take 9 + the first hour of renting to get [B]10 total hours[/B].
Check our work:
$7.95 * 9.5 + $19.50
$71.55 + $19.50 = $91.05

The first plan has $14 monthly fee and charges an additional $.14 for each minute of calls. The seco

The first plan has $14 monthly fee and charges an additional $.14 for each minute of calls. The second plan had a $21 monthly fee and charges an additional $.10 for each minute of calls. For how many minutes of calls will the cost of the two plans be equal?
Set up the cost equation C(m) for the first plan, where m is the amount of minutes you use
C(m) = 0.14m + 14
Set up the cost equation C(m) for the second plan, where m is the amount of minutes you use
C(m) = 0.10m + 21
Set them equal to each other:
0.14m + 14 = 0.10m + 21
[URL='https://www.mathcelebrity.com/1unk.php?num=0.14m%2B14%3D0.10m%2B21&pl=Solve']Typing this equation into our search engine[/URL], we get:
m = [B]175[/B]

The volleyball team and the wrestling team at Clarksville High School are having a joint car wash t

The volleyball team and the wrestling team at Clarksville High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $4 per car. In addition, they have already brought in $81 from past fundraisers. The wrestling team has raised $85 in the past, and they are making $2 per car today. After washing a certain number of cars together, each team will have raised the same amount in total. What will that total be? How many cars will that take?
Set up the earnings equation for the volleyball team where w is the number of cars washed:
E = Price per cars washed * w + past fundraisers
E = 4w + 81
Set up the earnings equation for the wrestling team where w is the number of cars washed:
E = Price per cars washed * w + past fundraisers
E = 2w + 85
If the raised the same amount in total, set both earnings equations equal to each other:
4w + 81 = 2w + 85
Solve for [I]w[/I] in the equation 4w + 81 = 2w + 85
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 4w and 2w. To do that, we subtract 2w from both sides
4w + 81 - 2w = 2w + 85 - 2w
[SIZE=5][B]Step 2: Cancel 2w on the right side:[/B][/SIZE]
2w + 81 = 85
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 81 and 85. To do that, we subtract 81 from both sides
2w + 81 - 81 = 85 - 81
[SIZE=5][B]Step 4: Cancel 81 on the left side:[/B][/SIZE]
2w = 4
[SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE]
2w/2 = 4/2
w = [B]2 <-- How many cars it will take
[/B]
To get the total earnings, we take either the volleyball or wrestling team's Earnings equation and plug in w = 2:
E = 4(2) + 81
E = 8 + 81
E = [B]89 <-- Total Earnings[/B]

There are 50 pairs of pants. One-half of the pants are black. One-fifth of the pants are tan. How ma

There are 50 pairs of pants. One-half of the pants are black. One-fifth of the pants are tan. How many pairs of pants are not black or tan.
First, determine what fraction of pants are black and tan:
1/2 + 1/5
Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F2&frac2=1%2F5&pl=Add']fraction addition calculator[/URL], we get 7/10.
So the rest of the pants are 1 - 7/10.
1 can be written as 10/10.
So we have 10/10 - 7/10 = 3/10
3/10 * 50 = 150/10 = [B]15[/B]

Three people went to lunch and bought a large meal which they all split. The total cost, including t

Three 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]

To ship a package with UPS, the cost will be $7 for the first pound and $0.20 for each additional po

To ship a package with UPS, the cost will be $7 for the first pound and $0.20 for each additional pound. To ship a package with FedEx, the cost will be $5 for the first pound and $0.30 for each additional pound. How many pounds will it take for UPS and FedEx to cost the same? If you needed to ship a package that weighs 8 lbs, which shipping company would you choose and how much would you pay?
[U]UPS: Set up the cost function C(p) where p is the number of pounds:[/U]
C(p) = Number of pounds over 1 * cost per pounds + first pound
C(p) = 0.2(p - 1) + 7
[U]FedEx: Set up the cost function C(p) where p is the number of pounds:[/U]
C(p) = Number of pounds over 1 * cost per pounds + first pound
C(p) = 0.3(p - 1) + 5
[U]When will the costs equal each other? Set the cost functions equal to each other:[/U]
0.2(p - 1) + 7 = 0.3(p - 1) + 5
0.2p - 0.2 + 7 = 0.3p - 0.3 + 5
0.2p + 6.8 = 0.3p + 4.7
To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.2p%2B6.8%3D0.3p%2B4.7&pl=Solve']type it in our search engine[/URL] and we get:
p = [B]21
So at 21 pounds, both UPS and FedEx costs are equal
[/B]
Now, find out which shipping company has a better rate at 8 pounds:
[U]UPS:[/U]
C(8) = 0.2(8 - 1) + 7
C(8) = 0.2(7) + 7
C(8) = 1.4 + 7
C(8) = 8.4
[U]FedEx:[/U]
C(8) = 0.3(8 - 1) + 5
C(8) = 0.3(7) + 5
C(8) = 2.1 + 5
C(8) = [B]7.1[/B]
[B]Therefore, FedEx is the better cost at 8 pounds since the cost is lower[/B]
[B][/B]

True False Equations

Determines if a set of addition and subtraction of numbers on each side of an equation are equivalent.
Also known as true or false equations

Tyrese’s sister is 41 inches tall. A ride at the amusement park states that riders must be at least

Tyrese’s sister is 41 inches tall. A ride at the amusement park states that riders must be at least 52 inches tall to ride. Which statements describe how much taller Tyrese’s sister must be to ride?
Let h be the required additional height.
The phrase [I]at least[/I] means an inequality, using the >= sign, so we have:
h + 41 >= 52
If we want another way to express this, we [URL='https://www.mathcelebrity.com/1unk.php?num=h%2B41%3E%3D52&pl=Solve']type this inequality into our math engine[/URL] and we get:
[B]h >= 11[/B]

Vectors

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.

Whitney has already baked 2 cakes, and she can bake 1 cake with each additional stick of butter she

Whitney has already baked 2 cakes, and she can bake 1 cake with each additional stick of butter she buys. Write an equation that shows the relationship between the number of additional sticks of butter s and the number of cakes c.
[LIST]
[*]Let c, the number of cakes, be represented by f(s) where s are the number of sticks of butter.
[*]We already have 2 cakes to start, and each additional stick of butter gets us one more cake.
[/LIST]
f(s) = 1s + 2
Simplify, since 1s is just s
[B]f(s) = s + 2[/B]

writing and solving equations

My daughter is having issues with a math problem for her homework. she tells me that I am doing it wrong but I am getting the correct answer... Can you please look at it and see if i am correct?
The problem is:
A painter charges $15.35 per hour, plus an additional amount for supplies. If he made $141.73 on a job where he worked 4 hours, how much did the supplies cost?
I have the equation as: $15.35 * 4 = $141.73 - x ... I got the answer of $80.33 for supplies
She is telling me that the teacher is wanting her to do the PEMDAS backwards but that is not working out for her and I am not understanding that at all. Any suggestions would help out
Thanks,
Tina

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 are parking your car in a garage. The first hour is free but every additional hour is 2 dollars.

You are parking your car in a garage. The first hour is free but every additional hour is 2 dollars. You parked for 3.25 hours. What is the cost?
[U]Calculate the number of paid hours:[/U]
Paid Hours = Total Hours - 1 (since first hour is free)
Paid Hours = 3.25 - 1
Paid Hours = 2.25
[U]Calculate the total cost:[/U]
Total Cost = Hourly Rate * Paid Hours
Total Cost = 2 * 2.25
Paid Hours = [B]$4.50[/B]

You started this year with $491 saved and you continue to save an additional $11 per month. Write an

You started this year with $491 saved and you continue to save an additional $11 per month. Write an algebraic expression to represent the total amount of money saved after m months.
Set up a savings function for m months
[B]S(m) = 491 + 11m[/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]