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1/9 of all sales were for cash. If cash sales were $59,000, what were the total sales?

1/9 of all sales were for cash. If cash sales were $59,000, what were the total sales?
Let sales be s. We're given:
s/9 = 59000
To solve this proportion for s, we [URL='https://www.mathcelebrity.com/prop.php?num1=s&num2=59000&den1=9&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
s = [B]531000[/B]

3 cases of fresh apples that cost $21.95 per case with 20% off and a 7.5% sales tax

3 cases of fresh apples that cost $21.95 per case with 20% off and a 7.5% sales tax
Figure out the total cost before the discount:
Total Cost before discount = Cases * Price per case
Total Cost before discount = 3 cases * $21.95 per case
Total Cost before discount = $65.85
Now, find the discounted value of the apples:
Discounted Apple Price = Total Cost before discount * (1 - discount percent)
Discounted ApplesPrice = $65.85 * (1 - 0.2) <-- 20% is the same as 0.2
Discounted ApplesPrice = $65.85 * 0.8
Discounted ApplesPrice = $52.68
Now, apply the sales tax to this discounted value to get the total bill:
Total Bill = Discounted Apple Price * (1 + tax rate)
Total Bill = $52.68 * (1 + .075) <-- 7.5% = 0.075
Total Bill = $52.68 * 1.075
Total Bill = [B]$56.63[/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 $750 television is on sale for 30% off. There is a 7% sales tax on the television. How much do you

A $750 television is on sale for 30% off. There is a 7% sales tax on the television. How much do you pay?
30% off:
750(1 - 0.3)
750(0.7) = 525
Now, add 7% sales tax
525 * (1.07) = [B]561.75[/B]

A 6000 seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each pri

A 6000 seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $188,800?
Let x be the number of $24 tickets, and y be the number of $40 tickets. We have:
[LIST=1]
[*]24x + 40y = 188,800
[*]x + y = 6,000
[*]Rearrange (2) to solve for x: x = 6000 - y
[*]Plug in (3) to (1):
[/LIST]
24(6000 - y) + 40y = 188800
144,000 - 24y + 40y = 188,800
16y + 144,000 = 188,800
Subtract 144,000 from each side:
16y = 44,800
Divide each side by 16
y = 2,800 ($40 tickets)
Plug this into (2)
x + 2,800 = 6000
Subtract 2,800 from each side:
x = 3,200 ($24 tickets)

A bakery offers a sale price of $3.50 for 4 muffins. What is the price per dozen?

A bakery offers a sale price of $3.50 for 4 muffins. What is the price per dozen?
1 dozen = 12 muffins
What this problem is really asking, $3.50 for 4 muffins. Let p be the price for 12 muffins (1 dozen). Set up a proportion of cost to muffins.
3.50/4 = p/12
Using our math engine, we [URL='https://www.mathcelebrity.com/prop.php?num1=3.50&num2=p&den1=4&den2=12&propsign=%3D&pl=Calculate+missing+proportion+value']type this proportion into our search box[/URL] and get:
p = [B]10.5 muffins
[MEDIA=youtube]ccY7yDkKvzs[/MEDIA][/B]

A bakery sells 5800 muffins in 2010. The bakery sells 7420 muffins in 2015. Write a linear model tha

A bakery sells 5800 muffins in 2010. The bakery sells 7420 muffins in 2015. Write a linear model that represents the number y of muffins that the bakery sells x years after 2010.
Find the number of muffins sold after 2010 through 2015:
7,420 - 5,800 = 1,620
Now, since the problem states a linear sales model, we need to determine the sales per year:
1,620 muffins sold since 2010 / 5 years = 324 muffins per year.
Build our linear model:
[B]y = 5,800 + 324x
[/B]
Reading this out loud, we start with 5,800 muffins at the end of 2010, and we add 324 more muffins for each year after 2010.

A bedroom set that normally sells for $1100 is on sale for 15% off. If sales tax rate is 2%, what is

A bedroom set that normally sells for $1100 is on sale for 15% off. If sales tax rate is 2%, what is the total price of the bedroom set if it is bought while on sale?
[U]Calculate the sale price:[/U]
Sale Price = Normal Price * (1 - Sales Percentage)
[U]With our sales percentage of 15% = 0.15, we have:[/U]
Sale Price = 1100 * (1 - 0.15)
Sale Price = 1100 * (0.85)
Sale Price = 935
[U]Calculate post tax amount:[/U]
Post tax amount = Sale Price * (1 + Tax Percentage)
[U]With our tax percentage of 2% = 0.02, we have:[/U]
Post tax amount = 935 * (1 + 0.02)
Post tax amount = 935 * (1.02)
Post tax amount = [B]$953.70[/B]

A bicycle helmet is priced at $18.50. If it is on sale for 10% off and there is 7% sales tax, how mu

A bicycle helmet is priced at $18.50. If it is on sale for 10% off and there is 7% sales tax, how much will it cost after tax?
[U]Calculate percent off first:[/U]
10% off means 90% off the price
$18.50 * (1 - 0.1)
$18.50 * (0.9) = 16.65
[U]Now, add 7% sales tax to the discounted price[/U]
Price after sales tax = Discounted Price * 1.07
Price after sales tax = 16.65(1.07)
[B]Price after sales tax = 17.82[/B]

A bicycle store costs $2750 per month to operate. The store pays an average of $45 per bike. The a

A bicycle store costs $2750 per month to operate. The store pays an average of $45 per bike. The average selling price of each bicycle is $95. How many bicycles must the store sell each month to break even?
Let the number of bikes be b.
Set up our cost function, where it costs $45 per bike to produce
C(b) = 45b
Set up our revenue function, where we earn $95 per sale for each bike:
R(b) = 95b
Set up our profit function, which is how much we keep after a sale:
P(b) = R(b) - C(b)
P(b) = 95b - 45b
P(b) = 50b
The problem wants to know how many bikes we need to sell to break-even. Note: break-even means profit equals operating cost, which in this case, is $2,750. So we set our profit function of 50b equal to $2,750
50b = 2750
[URL='https://www.mathcelebrity.com/1unk.php?num=50b%3D2750&pl=Solve']We type this equation into our search engine[/URL], and we get:
b = [B]55[/B]

A bike is purchased for $200 and sold for $150. Determine the percentage of profit or loss.

A bike is purchased for $200 and sold for $150. Determine the percentage of profit or loss.
[U]Since sale price is less than purchase price, we have a loss:[/U]
Loss = Sale Price - Purchase Price
Loss = 150 - 200
Loss = -50
[U]Calculate percent loss:[/U]
Percent Loss = 100% * Loss / Purchase Price
Percent Loss = 100% * -50/200
Percent Loss = 100% *- 1/4
Percent Loss = [B]-25%[/B]

A bill at a resturant came to $95.75. There is 7.5% sales tax added on. You want to leave a 20% tip

A bill at a resturant came to $95.75. There is 7.5% sales tax added on. You want to leave a 20% tip to the total bill, after tax. How much money will you need to leave for the bill altogether?
Since the tip is [I]after tax[/I], we have:
Total Bill = Pre-tax Bill * (1 + Sales Tax Percent) * (1 + Tip Percent)
Total Bill = $95.75 * (1 + 0.07) * (1 + 0.2)
Total Bill = $95.75 * 1.07 * 1.2
Total Bill = [B]$122.94[/B]

A car is purchased for $19000. After each year, the resale value decreases by 30% . What will the re

A car is purchased for $19000. After each year, the resale value decreases by 30% . What will the resale value be after 4 years?
Set up a book value function B(t) where t is the number of years after purchase date. If an asset decreases by 30%, we subtract it from the original 100% of the starting value at time t:
B(t) = 19,000(1-0.3)^t
Simplifying this, we get:
B(t) = 19,000(0.7)^t <-- I[I]f an asset decreases by 30%, it keeps 70% of it's value from the prior period[/I]
The problem asks for B(4):
B(4) = 19,000(0.7)^4
B(4) = 19,000(0.2401)
B(4) = [B]4,561.90[/B]

A car is purchased for 27,000$. After each year the resale value decreases by 20%. What will the res

A car is purchased for 27,000$. After each year the resale value decreases by 20%. What will the resale value be after 3 years?
If it decreases by 20%, it holds 100% - 20% = 80% of the value each year. So we have an equation R(t) where t is the time after purchase:
R(t) = 27,000 * (0.8)^t
The problem asks for R(3):
R(3) = 27,000 * (0.8)^3
R(3) = 27,000 * 0.512
R(3) = [B]13.824[/B]

A car salesman earns $800 per month plus a 10% commission on the value of sales he makes for the mon

A car salesman earns $800 per month plus a 10% commission on the value of sales he makes for the month. If he is aiming to earn a minimum of $3200 a month, what is the possible value of sales that will enable this?
to start, we have:
[LIST]
[*]Let the salesman's monthly sales be s.
[*]With a 10% discount as a decimal of 0.1
[*]The phrase [I]a minimum[/I] also means [I]at least[/I] or [I]greater than or equal to[/I]. This tells us we want an inequality
[*]We want 10% times s + 800 per month is greater than or equal to 3200
[/LIST]
We want the inequality:
0.1s + 800 >= 3200
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.1s%2B800%3E%3D3200&pl=Solve']type this inequality into our search engine[/URL] and we get:
[B]s >= 24000[/B]

A coat is on sale for 35% off. The regular price of the coat is p. Write and simplify and expression

A coat is on sale for 35% off. The regular price of the coat is p. Write and simplify and expression to represent the sale price of the coat. Show your work.
The Sale price of the coat is:
S = p(1 - 0.35) <-- Since 35% is 0.35 as a decimal
[B]S = 0.65p[/B]

A company had sales of $19,808 million in 1999 and $28,858 million in 2007. Use the Midpoint Formula

A company had sales of $19,808 million in 1999 and $28,858 million in 2007. Use the Midpoint Formula to estimate the sales in 2003
2003 is the midpoint of 1999 and 2007, so we use our [URL='https://www.mathcelebrity.com/mptnline.php?ept1=19808&empt=&ept2=28858&pl=Calculate+missing+Number+Line+item']midpoint calculator[/URL] to get:
[B]24,333[/B] sales in 2003

A company has a fixed cost of $26,000 / month when it is producing printed tapestries. Each item tha

A company has a fixed cost of $26,000 / month when it is producing printed tapestries. Each item that it makes has its own cost of $34. One month the company filled an order for 2400 of its tapestries, selling each item for $63. How much profit was generated by the order?
[U]Set up Cost function C(t) where t is the number of tapestries:[/U]
C(t) = Cost per tapestry * number of tapestries + Fixed Cost
C(t) = 34t + 26000
[U]Set up Revenue function R(t) where t is the number of tapestries:[/U]
R(t) = Sale Price * number of tapestries
R(t) = 63t
[U]Set up Profit function P(t) where t is the number of tapestries:[/U]
P(t) = R(t) - C(t)
P(t) = 63t - (34t + 26000)
P(t) = 63t - 34t - 26000
P(t) = 29t - 26000
[U]The problem asks for profit when t = 2400:[/U]
P(2400) = 29(2400) - 26000
P(2400) = 69,600 - 26,000
P(2400) = [B]43,600[/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 company makes toy boats. Their monthly fixed costs are $1500. The variable costs are $50 per boat.

A company makes toy boats. Their monthly fixed costs are $1500. The variable costs are $50 per boat. They sell boats for $75 a piece. How many boats must be sold each month to break even?
[U]Set up Cost function C(b) where t is the number of tapestries:[/U]
C(b) = Cost per boat * number of boats + Fixed Cost
C(b) = 50b + 1500
[U]Set up Revenue function R(b) where t is the number of tapestries:[/U]
R(b) = Sale Price * number of boats
R(b) = 75b
[U]Break even is where Revenue equals Cost, or Revenue minus Cost is 0, so we have:[/U]
R(b) - C(b) = 0
75b - (50b + 1500) = 0
75b - 50b - 1500 = 0
25b - 1500 = 0
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=25b-1500%3D0&pl=Solve']type this equation in our math engine[/URL] and we get:
b = [B]60[/B]

A company specializes in personalized team uniforms. It costs the company $15 to make each uniform a

A company specializes in personalized team uniforms. It costs the company $15 to make each uniform along with their fixed costs at $640. The company plans to sell each uniform for $55.
[U]The cost function for "u" uniforms C(u) is given by:[/U]
C(u) = Cost per uniform * u + Fixed Costs
[B]C(u) = 15u + 640[/B]
Build the revenue function R(u) where u is the number of uniforms:
R(u) = Sale Price per uniform * u
[B]R(u) = 55u[/B]
Calculate break even function:
Break even is where Revenue equals cost
C(u) = R(u)
15u + 640 = 55u
To solve for u, we [URL='https://www.mathcelebrity.com/1unk.php?num=15u%2B640%3D55u&pl=Solve']type this equation into our search engine[/URL] and we get:
u = [B]16
So we break even selling 16 uniforms[/B]

a computer is purchased for 800 and each year the resale value decreases by 25% what will be the res

a computer is purchased for 800 and each year the resale value decreases by 25% what will be the resale value after 4 years
Let the resale in year y be R(y). We have:
R(y) = 800 * (1 - 0.25)^y
R(y) = 800 * (0.75)^y
The problem asks for R(4):
R(4) = 800 * (0.75)^4
R(4) = 800 * 0.31640625
R(4) = [B]$253.13[/B]

A computer was on sale. The original cost of the computer was $900. It’s on sale for 5/6 the price.

A computer was on sale. The original cost of the computer was $900. It’s on sale for 5/6 the price. How much is the computer now?
We want 5/6 of 900. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=900&frac2=5/6&pl=Multiply']type this in our search engine[/URL] and we get:
[B]750[/B]

A corn refining company produces corn gluten cattle feed at a variable cost of $84 per ton. If fixe

A corn refining company produces corn gluten cattle feed at a variable cost of $84 per ton. If fixed costs are $110,000 per month and the feed sells for $132 per ton, how many tons should be sold each month to have a monthly profit of $560,000?
[U]Set up the cost function C(t) where t is the number of tons of cattle feed:[/U]
C(t) = Variable Cost * t + Fixed Costs
C(t) = 84t + 110000
[U]Set up the revenue function R(t) where t is the number of tons of cattle feed:[/U]
R(t) = Sale Price * t
R(t) = 132t
[U]Set up the profit function P(t) where t is the number of tons of cattle feed:[/U]
P(t) = R(t) - C(t)
P(t) = 132t - (84t + 110000)
P(t) = 132t - 84t - 110000
P(t) = 48t - 110000
[U]The question asks for how many tons (t) need to be sold each month to have a monthly profit of 560,000. So we set P(t) = 560000:[/U]
48t - 110000 = 560000
[U]To solve for t, we [URL='https://www.mathcelebrity.com/1unk.php?num=48t-110000%3D560000&pl=Solve']type this equation into our search engine[/URL] and we get:[/U]
t =[B] 13,958.33
If the problem asks for whole numbers, we round up one ton to get 13,959[/B]

A dress is on sale for $33. This is 3/5 of the regular price. What is the regular price?

A dress is on sale for $33. This is 3/5 of the regular price. What is the regular price?
Original price is p. We have:
3p/5 = 33
Cross multiply using our [URL='http://www.mathcelebrity.com/prop.php?num1=3p&num2=33&den1=5&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get [B]p = 55[/B].

A house sold for $200,000 and the real estate agent earned a commission of $10,200.00. Find the comm

A house sold for $200,000 and the real estate agent earned a commission of $10,200.00. Find the commission rate.
Commission Rate = 100 * Commission Amount / Sale Price
Commission Rate = 100 * 10200/20000
Commission Rate = 100 * 0.051
Commission Rate = [B]5.51%[/B]

A laptop is purchased for $1700. After each year, the resale value decreases by 25%. What will be th

A laptop is purchased for $1700. After each year, the resale value decreases by 25%. What will be the resale value after 5 years?
[U]Let R(t) be the Resale value at time t:[/U]
R(t) = 1,700(1 - 0.25)^t
[U]We want R(5)[/U]
R(5) = 1,700(1 - 0.25)^5
R(5) =1,700(0.75)^5
R(5) =1,700 * 0.2373
R(5) = [B]$403.42[/B]

A limo costs $85 to rent for 3 hours plus a 7% sales tax. What is the total cost to rent the limo fo

A limo costs $85 to rent for 3 hours plus a 7% sales tax. What is the total cost to rent the limo for 6 hours?
Determine the number of 3 hour blocks:
3 hour blocks = Total Rental Time / 3
3 hour blocks = 6 hours / 3
3 hour blocks = 2
With 7% = 0.07, we have:
Total Cost = $85 * / 3 hours * 2 (3 hour blocks) * 1.07
Total Cost = 85 * 2 * 1.07
Total Cost = [B]181.9[/B]

A local Dunkin’ Donuts shop reported that its sales have increased exactly 16% per year for the last

A local Dunkin’ Donuts shop reported that its sales have increased exactly 16% per year for the last 2 years. This year’s sales were $80,642. What were Dunkin' Donuts' sales 2 years ago?
Declare variable and convert numbers:
[LIST]
[*]16% = 0.16
[*]let the sales 2 years ago be s.
[/LIST]
s(1 + 0.16)(1 + 0.16) = 80,642
s(1.16)(1.16) = 80,642
1.3456s = 80642
Solve for [I]s[/I] in the equation 1.3456s = 80642
[SIZE=5][B]Step 1: Divide each side of the equation by 1.3456[/B][/SIZE]
1.3456s/1.3456 = 80642/1.3456
s = 59930.142687277
s = [B]59,930.14[/B]

A man bought a mobile phone for $800 and sold it for $1000. What was his profit as a percentage of t

A man bought a mobile phone for $800 and sold it for $1000. What was his profit as a percentage of the cost price
Calculate Profit:
Profit = Sales Price - Cost
Profit = 1000 - 800
Profit = 200
Calculate profit percentage:
Profit Percentage = Profit * 100 / Cost
Profit Percentage = 800 * 100 / 200
Profit Percentage = [B]400%[/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 movie theater has a seating capacity of 143. The theater charges $5.00 for children, $7.00 for stu

A movie theater has a seating capacity of 143. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1030, How many children, students, and adults attended?
Let c be the number of children's tickets, s be the number of student's tickets, and a be the number of adult's tickets. We have 3 equations:
[LIST=1]
[*]a + c + s = 143
[*]a = 0.5c
[*]12a + 5c + 7s =1030
[/LIST]
Substitute (2) into (1)
0.5c + c + s = 143
1.5c + s = 143
Subtract 1.5c from each side
4. s = 143 - 1.5c
Now, take (4) and (2), and plug it into (3)
12(0.5c) + 5c + 7(143 - 1.5c) = 1030
6c + 5c + 1001 - 10.5c = 1030
Combine like terms:
0.5c + 1001 = 1030
Use our [URL='http://www.mathcelebrity.com/1unk.php?num=0.5c%2B1001%3D1030&pl=Solve']equation calculator[/URL] to get [B]c = 58[/B].
Plug this back into (2)
a = 0.5(58)
[B]a = 29
[/B]
Now take the a and c values, and plug it into (1)
29 + 58 + s = 143
s + 87 = 143
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=s%2B87%3D143&pl=Solve']equation calculator[/URL] again, we get [B]s = 56[/B].
To summarize, we have:
[LIST]
[*]29 adults
[*]58 children
[*]56 students
[/LIST]

A new car worth $30,000 is depreciating in value by $3,000 per year. After how many years will the c

A new car worth $30,000 is depreciating in value by $3,000 per year. After how many years will the cars value be $9,000
Step 1, the question asks for Book Value. Let y be the number of years since purchase.
We setup an equation B(y) which is the Book Value at time y.
B(y) = Sale Price - Depreciation Amount * y
We're given Sale price = $30,000, depreciation amount = 3,000, and B(y) = 9000
30000 - 3000y = 9000
To solve for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=30000-3000y%3D9000&pl=Solve']type this in our math engine[/URL] and we get:
y = [B]7
[/B]
To check our work, substitute y = 7 into B(y)
B(7) = 30000 - 3000(7)
B(7) = 30000 - 21000
B(7) = 9000
[MEDIA=youtube]oCpBBS7fRYs[/MEDIA]

A pair of jeans are priced at $129.99 there is a discount of 20% and sales tax of 8% what is the fin

A pair of jeans are priced at $129.99 there is a discount of 20% and sales tax of 8% what is the final cost
[U]Calculate discounted price:[/U]
Discounted price = Full price * (100% - discount percent)
Discounted price = 129.99 * (100% - 20%)
Discounted price = 129.99 * 80%
Since 80% = 0.8, we have:
Discounted price = 129.99 * 0.8
Discounted price = 103.99
[U]Calculate after tax cost:[/U]
Tax Rate = Tax percent/100
Tax Rate = 8/100
Tax Rate = 0.08
After Tax cost = Discounted price * (1 + Tax rate)
After Tax cost = 103.99 * (1 + 0.08)
After Tax cost = 103.99 * 1.08
After Tax cost = [B]112.31[/B]

A pawn broker buys a tv and a computer for $600. He sells the computer at a markup of 30% and the tv

A pawn broker buys a tv and a computer for $600. He sells the computer at a markup of 30% and the tv at a markup of 20%. If he makes a profit of $165 on the sale of the two items, what did he pay for the computer?
Let c be the price of the computer and t be the price of the tv. WE have:
[LIST=1]
[*]c + t = 600
[*]c(1.3) + t(1.2) = 765 <-- (600 + 165 profit)
[/LIST]
Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+t+%3D+600&term2=1.3c+%2B+1.2t+%3D+765&pl=Cramers+Method']simultaneous equation calculator[/URL], we get:
[B]c = 450[/B]
t = 150

A person paid $60 for a vase at an estate auction. She resold it to an antiques dealer for $50. What

A person paid $60 for a vase at an estate auction. She resold it to an antiques dealer for $50. What was her profit or loss
She lost, since the sale price was less than the purchase price.
The loss is calculated as:
50 - 60 = [B]-$10[/B]

A pet supply chain called pet city has 15 hamsters and 12 gerbils for sale at its seaside location.

A pet supply chain called pet city has 15 hamsters and 12 gerbils for sale at its seaside location. At its livingston location there are 19 hamsters and 10 gerbils. Which location has a lower ratio of hamsters to gerbils?
Seaside ratio
15/12 = 1.25
Livingston ratio
19/10 = 1.9
Since 1.25 < 1.9, Seaside has the lower ratio of hamsters to gerbils

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 property sold for $198,000 with a listing commission of 8%. The selling office is to receive 40% o

A property sold for $198,000 with a listing commission of 8%. The selling office is to receive 40% of the total commission. How much will the listing salesperson receive if she is paid 60% of the amount retained by listed broker.
[U]Calculate commission amount:[/U]
Commission amount = Sale Price * Commission Percent
Commission amount = 198,000 * 8%
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=8&den1=198000&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Commission amount [/URL]= 15,840
[U]Calculate listing salesperson commission amount:[/U]
Listing salesperson commission amount = Commission Amount * Listing salesperson Percent
Listing salesperson commission amount = 15,840 * 60%
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=60&den1=15840&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Listing salesperson commission amount[/URL] = [B]9,504[/B]

A real estate agency receives 3.5% commission on the first $100,000 of a sale and 2.25% on the remai

A real estate agency receives 3.5% commission on the first $100,000 of a sale and 2.25% on the remainder. How much commission is received on the sale of a $450,000 property?
Calculate commission on first $100,000 (Commission 1):
Commission 1 = $100,000 * 0.035
Commission 1 = $3,500
Calculate commission on the remainder (Commission 2):
Commission 2 = 0.025 * ($450,000 - $100,000)
Commission 2 = 0.025 * ($350,000)
Commission 2 = $8,750
Calculate Total Commission:
Total Commission = Commission 1 + Commission 2
Total Commission = $3,500 + $8,750
Total Commission = [B]$12,250[/B]

A real estate agent sells a house for $229,605. A sales commission of 6% is charged. The agent gets

A real estate agent sells a house for $229,605. A sales commission of 6% is charged. The agent gets 45% of this commission. How much money does the agent get?
The agents Commission (C) is:
C = Sale price * sales commission percent * agent commission percent
Since 6% = 0.06 and 45% = 0.45, we have:
C = 229605 * 0.06 * 0.45
C = [B]6,199.34[/B]

A realtor makes an annual salary of $25000 plus a 3% commission on sales. If a realtor's salary is $

A realtor makes an annual salary of $25000 plus a 3% commission on sales. If a realtor's salary is $67000, what was the amount of her sales?
Total post-salary pay = $67,000 - $25,000 = $42,000
Let Sales be s.
So 0.03s = $42,000
Divide each side by 0.03
s = $1,400,000

a sales rep can generate $1,900,000 in business annually. What rate of commission does he need to ea

a sales rep can generate $1,900,000 in business annually. What rate of commission does he need to earn $30,000?
We need a commission percent p where:
1900000 * p = 30000
To solve for p, we type this equation into our search engine and we get:
p = 0.0158 or [B]1.58%[/B]

A salesperson earns a commission of $364 for selling $2600 in merchandise. Find the commission rate.

A salesperson earns a commission of $364 for selling $2600 in merchandise. Find the commission rate. Write your answer as a percentage.
Commission percentage = Commission Amount / Sales Price
Commission percentage = 364 / 2600
Commission percentage = 0.14
Multiply by 100 to get the percentage:
0.14 * 100 = [B]14%[/B]

A salesperson receives a base salary of $300 per week and a commission of 15% on all sales over $5,0

A salesperson receives a base salary of $300 per week and a commission of 15% on all sales over $5,000. If x represents the salesperson’s weekly sales, express the total weekly earnings E(x) as a function of x and simplify the expression. Then find E(2,000) and E(7,000) and E(10,000).
15% as a decimal is written as 0.15.
Build our weekly earnings function
E(x) = Commission + Base Salary
E(x) = 0.15(Max(0, x - 5000)) + 300
Now find the sales salary for 2,000, 7,000, and 10,000 in sales
E(2,000) = 0.15(Max(0,2000 - 5000)) + 300
E(2,000) = 0.15(Max(0,-3000)) + 300
E(2,000) = 0.15(0) + 300
[B]E(2,000) = 300
[/B]
E(7,000) = 0.15(Max(0,7000 - 5000)) + 300
E(7,000) = 0.15(Max(0,2000)) + 300
E(7,000) = 0.15(2,000) + 300
E(7,000) = 300 + 300
[B][B]E(7,000) = 600[/B][/B]
E(10,000) = 0.15(Max(0,10000 - 5000)) + 300
E(10,000) = 0.15(Max(0,5000)) + 300
E(10,000) = 0.15(5,000) + 300
E(10,000) = 750+ 300
[B][B]E(10,000) = 1,050[/B][/B]

A Salesperson receives a weekly salary of $100 plus a 5.5% commission on sales. Her salary last week

A Salesperson receives a weekly salary of $100 plus a 5.5% commission on sales. Her salary last week was $1090. What were her sales that week?
$1,090 - 100 = $990.
This is her commission.
Let s = Sales.
So 0.055s = $990
Divide each side by 0.055.
s = $18,000

A salesperson works 40 hours per week at a job where he has two options for being paid. Option A is

A salesperson works 40 hours per week at a job where he has two options for being paid. Option A is an hourly wage of $24. Option B is a commission rate of 4% on weekly sales. How much does he need to sell this week to earn the same amount with the two options?
Option A payment function:
24h
With a 40 hour week, we have:
24 * 40 = 960
Option B payment function with sales amount (s):
0.04s
We want to know the amount of sales (s) where Option A at 40 hours = Option B. So we set both equal to each other:
0.04s = 960
To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.04s%3D960&pl=Solve']type it in our math engine[/URL] and we get:
s = [B]24,000[/B]

A school theater group is selling candy to raise funds in order to put on their next performance. Th

A school theater group is selling candy to raise funds in order to put on their next performance. The candy cost the group $0.20 per piece. Plus, there was a $9 shipping and handling fee. The group is going to sell the candy for $0.50 per piece. How many pieces of candy must the group sell in order to break even?
[U]Set up the cost function C(p) where p is the number of pieces of candy.[/U]
C(p) = Cost per piece * p + shipping and handling fee
C(p) = 0.2p + 9
[U]Set up the Revenue function R(p) where p is the number of pieces of candy.[/U]
R(p) = Sale price * p
R(p) = 0.5p
Break-even means zero profit or loss, so we set the Cost Function equal to the Revenue Function
0.2p + 9 = 0.5p
To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.2p%2B9%3D0.5p&pl=Solve']type it in our math engine[/URL] and we get:
p = [B]30[/B]

a shop has a sale of 1/5 off all items in stock. if the original price of a dress is £45, what would

a shop has a sale of 1/5 off all items in stock. if the original price of a dress is £45, what would be its sale price?
[URL='https://www.mathcelebrity.com/fraction.php?frac1=45&frac2=1/5&pl=Multiply']1/5 of 45[/URL] = 9
45 - 9 = [B]36[/B]

A sports store near Big Bear Lake is having a 20% off sale on all water skis. What will the sale pri

A sports store near Big Bear Lake is having a 20% off sale on all water skis. What will the sale price be for water skis which regularly sell for $248?
[U]Calculate Sale Price:[/U]
Sale Price = Full Price * (1 - sale discount)
Sale Price = 248 * (1 - 0.2) <-- since 20% is 0.2
Sale Price = 248 * (0.8)
Sale Price = [B]198.40[/B]

A store is offering a 15% discount on all items. Write an equation relating the sale price S for an

A store is offering a 15% discount on all items. Write an equation relating the sale price S for an item to its list price L
If we give a discount of 15%, then we pay 100% - 15% = 85% of the list price. 85% as a decimal is 0.85, So we have:
L = 0.85S

A store is offering a 18% discount on all items. Write an equation relating the sale price S for an

A store is offering a 18% discount on all items. Write an equation relating the sale price S for an item to its list price L.
18% discount means we subtract 18% (0.18) as a decimal, from the 100% of the price:
S = L(1 - 0.18)
[B]S = 0.82L[/B]

A store manager must calculate the total number of winter hats available to sell in the store from a

A store manager must calculate the total number of winter hats available to sell in the store from a starting number of 293. In the past month, the store sold 43 blue hats, 96 black hats, 28 red hats, and 61 pink hats. The store received a shipment of 48 blue hats, 60 black hats, 18 red hats, and 24 pink hats. How many total hats does the store have for sale?
[LIST=1]
[*]We start with 293 hats
[*]We calculate the hats sold: (43 + 96 + 28 + 61) = 228
[*]We subtract Step 2 from Step 1 to get remaining hats before the shipment: 293 - 228 = 65
[*]Now we calculate the number of hats received in the shipment: (48 + 60 + 18 + 24) = 150
[*]We add Step 4 to Step 3: 65 + 150 = [B]215 hats for sale[/B]
[/LIST]

A store owner bought 240 cartons of eggs. The owner sold 5/8 of the eggs and set aside 5 cartons. Ho

A store owner bought 240 cartons of eggs. The owner sold 5/8 of the eggs and set aside 5 cartons. How many cartons of eggs did the owner have left to sale?
If the owner sold 5/8 of the eggs, they have 1 - 5/8 left.
1 = 8/8, so we have 8/8 - 5/8 = 3/8 left
3/8 (240 cartons) = 90 cartons remaining
The owner set aside 5 cartons.
We're left with 90 cartons - 5 cartons = [B]85 cartons[/B]

a store sells a certain toaster oven for 35. The store offers a 30% discount and charges 8% sales ta

a store sells a certain toaster oven for 35. The store offers a 30% discount and charges 8% sales tax. How much will the toaster oven cost?
[U]Calculate discounted price:[/U]
Discounted Price = Full Price * (1 - Discount Percent)
Since 30% = 0.3, we have
Discounted Price = 35 * (1 - 0.3)
Discounted Price = 35 * 0.7
Discounted Price = 24.5
Calculate after-tax amount:
After-tax amount = Discounted Price * (1 + Tax Percent)
Since 8% = 0.08, we have
Discounted Price = 24.5 * (1 + 0.08)
Discounted Price = 24.5 * 1.08
Discounted Price = [B]26.46[/B]

A sweater that you love costs $32. You really want the sweater but only have $35. If there’s a sales

A sweater that you love costs $32. You really want the sweater but only have $35. If there’s a sales tax of 4% on the item, do you have enough to buy the sweater?
Calculate after-tax amount:
After tax amount = Sale Price * (1 + sales tax percent)
After tax amount = 32 * (1 + 0.04) <-- Since 4% = 0.04
After tax amount = 32 * (1.04)
After tax amount = $33.28
[B]Yes[/B], since $33.28 is less than or equal to $35, you have enough to buy the sweater.

A toy company makes "Teddy Bears". The company spends $1500 for factory expenses plus $8 per bear. T

A toy company makes "Teddy Bears". The company spends $1500 for factory expenses plus $8 per bear. The company sells each bear for $12.00 each. How many bears must this company sell in order to break even?
[U]Set up the cost function C(b) where b is the number of bears:[/U]
C(b) = Cost per bear * b + factory expenses
C(b) = 8b + 1500
[U]Set up the revenue function R(b) where b is the number of bears:[/U]
R(b) = Sale Price per bear * b
R(b) = 12b
[U]Break-even is where cost equals revenue, so we set C(b) equal to R(b) and solve for b:[/U]
C(b) = R(b)
8b + 1500 = 12b
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=8b%2B1500%3D12b&pl=Solve']type this equation into our search engine[/URL] and we get:
b = [B]375[/B]

A TV that usually sells for $192.94 is on sale for 15% off. If sales tax on the TV is 6%, what is th

A TV that usually sells for $192.94 is on sale for 15% off. If sales tax on the TV is 6%, what is the price of the TV, including tax?
Find the discounted price: 15% off of 192.94
Discounted Price = 192.94 * (1 - 0.15) <-- 15% as a decimal is 0.15, and 1 is 100%, so we subtract to get 85% of the original price
Discounted Price =192.94(0.85)
Discounted Price = $164
Now, add in the sales tax of 6% to the Discounted Price
Price after sales tax = Discounted Price * 1.06
Price after sales tax = $164 * 1.06
[B]Price after sales tax = $173.84[/B]

A used book store also started selling used CDs and videos. In the first week, the store sold a comb

A used book store also started selling used CDs and videos. In the first week, the store sold a combination of 40 CDs and videos. They charged $4 per CD and $6 per video and the total sales were $180. Determine the total number of CDs and videos sold
Let c be the number of CDs sold, and v be the number of videos sold. We're given 2 equations:
[LIST=1]
[*]c + v = 40
[*]4c + 6v = 180
[/LIST]
You can solve this system of equations three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
No matter what method we choose, we get [B]c = 30, v = 10[/B].
Now let's check our work for both given equations for c = 30 and v = 10:
[LIST=1]
[*]30 + 10 = 40 <-- This checks out
[*]4c + 6v = 180 --> 4(30) + 6(10) --> 120 + 60 = 180 <-- This checks out
[/LIST]

A used book store also started selling used CDs and videos. In the first week, the store sold a comb

A used book store also started selling used CDs and videos. In the first week, the store sold a combination of 40 CDs and videos. They charged $4 per CD and $6 per video and the total sales were $180. Determine the total number of CDs and videos sold.
Let the number of cd's be c and number of videos be v. We're given two equations:
[LIST=1]
[*]c + v = 40
[*]4c + 6v = 180
[/LIST]
We can solve this system of equations using 3 methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
[B]c = 30
v = 10[/B]

A watch was bought for $250 and sold for $375. What was the profit on the sale of the watch?

A watch was bought for $250 and sold for $375. What was the profit on the sale of the watch?
Profit = Revenue (Sales) - Cost
Profit = $375 - $250
Profit = [B]$125[/B]

After a 33 percent reduction, you purchase a television for $281.40. What was the televisions price

After a 33 percent reduction, you purchase a television for $281.40. What was the televisions price before the reduction?
Using our [URL='http://www.mathcelebrity.com/markup.php?p1=++281.40&m=+33&p2=&pl=Calculate']markup/markdown calculator[/URL], we get:
Original Sale Price = [B]$374.26[/B]

Alexis is working at her schools bake sale. Each mini cherry pie sells for $4 and each mini peach pi

Alexis is working at her schools bake sale. Each mini cherry pie sells for $4 and each mini peach pie sells for $3. Alexis sells 25 pies and collects $84. How many pies of each kind does she sell?
Let each cherry pie be c and each peach pie be p. We have the following equations:
[LIST=1]
[*]c + p = 25
[*]4c + 3p = 84
[/LIST]
You can solve this system of equations 3 ways.
[URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c%2Bp%3D25&term2=4c+%2B+3p+%3D+84&pl=Substitution']Substitution Rule[/URL]
[URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c%2Bp%3D25&term2=4c+%2B+3p+%3D+84&pl=Elimination']Elimination Rule[/URL]
[URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c%2Bp%3D25&term2=4c+%2B+3p+%3D+84&pl=Cramers+Method']Cramers Rule[/URL]
No matter which way you choose, you get [B]c = 9 and p = 16[/B].

An item cost $370 before tax, and the sales tax is 25.90 what is the percentage?

An item cost $370 before tax, and the sales tax is 25.90 what is the percentage?
Sales Tax = Tax Amount/Original Bill
Sales Tax = 25.90/370
Sales Tax = 0.07
Multiply by 100 to convert to a percent, we have[B] 7%[/B]

An item costs $470 before tax, and the sales tax is $14.10. Find the sales tax rate. Write your answ

An item costs $470 before tax, and the sales tax is $14.10. Find the sales tax rate. Write your answer as a percentage.
Sales Tax Percent = 100% * Sales Tax / Before Tax Amount
Sales Tax Percent = 100% * 14.10 / 470
Sales Tax Percent = 100% * 0.03
Sales Tax Percent = [B]3%[/B]

As a salesperson you will earn $600 per month plus a commission of 20% of sales. Find the minimum am

As a salesperson you will earn $600 per month plus a commission of 20% of sales. Find the minimum amount of sales you need to make in order to receive a total income of at least $1500 per month.
Let the amount of sales be s. The phrase [I]at least[/I] means greater than or equal to. Since 20% is 0.2, We want to know when:
0.20s + 600 >= 1500
We [URL='https://www.mathcelebrity.com/1unk.php?num=0.20s%2B600%3E%3D1500&pl=Solve']type this inequality into our search engine to solve for s[/URL] and we get:
s >= [B]4500[/B]

As a salesperson, Laura earns a base salary of $72 per week plus a commission of 20% of sales. If sh

As a salesperson, Laura earns a base salary of $72 per week plus a commission of 20% of sales. If she had $75 in sales last week, what was her total pay?
Total Pay = Base Pay + Commission
Calculate Commission:
Commission = Commission Percent x Sales
Commission = 20% * 75
Commission = 15
Total Pay = Base Pay + Commission
Total Pay = 72 + 15
Total Pay = [B]$97[/B]

As a salesperson, Lauren earns a base salary of $94 per week plus a commission of 10% of sales. If s

As a salesperson, Lauren earns a base salary of $94 per week plus a commission of 10% of sales. If she had $90 in sales last week, what was her total pay?
[B][U]Use the Base plus Commission formula above[/U][/B]
Salary = Base Salary + 10%(Total Sales)
Salary = $94 + 0.1(90)
Salary = $94 + $9
Salary = [B]$103[/B]

As a salesperson, you are paid $50 per week plus $2 per sale. This week you want your pay to be at l

As a salesperson, you are paid $50 per week plus $2 per sale. This week you want your pay to be at least $100. What is the minimum number of sales you must make to earn at least $100?
Set up the inequality where s is the amount of sales you make:
50 + 2s >= 100
We use >= because the phrase [I]at least[/I] 100 means 100 or more
Subtract 50 from each side:
2s >= 50
Divide each side by 2
[B]s >= 25[/B]

At a carnival, the price of an adult ticket is $6 while a child ticket is $4. On a certain day, 30 m

At a carnival, the price of an adult ticket is $6 while a child ticket is $4. On a certain day, 30 more child tickets than adult tickets were sold. If a total of $6360 was collected from the total ticket sale that day, how many child tickets were sold?
Let the number of adult tickets be a. Let the number of child tickets be c. We're given two equations:
[LIST=1]
[*]c = a + 30
[*]6a + 4c = 6360
[/LIST]
Substitute equation (1) into equation (2):
6a + 4(a + 30) = 6360
Multiply through to remove parentheses:
6a + 4a + 120 = 6360
T[URL='https://www.mathcelebrity.com/1unk.php?num=6a%2B4a%2B120%3D6360&pl=Solve']ype this equation into our search engine[/URL] to solve for a and we get:
a = 624
Now substitute a = 624 back into equation (1) to solve for c:
c = 124 + 30
c = [B]154[/B]

At a homecoming football game, the senior class sold slices of pizza for $.75 each and hamburgers fo

At a homecoming football game, the senior class sold slices of pizza for $.75 each and hamburgers for $1.35 each. They sold 40 more slices of pizza than hamburgers, and sales totaled $292.5. How many slices of pizza did they sell
Let the number of pizza slices be p and the number of hamburgers be h. We're given two equations:
[LIST=1]
[*]p = h + 40
[*]1.35h + 0.75p = 292.50
[/LIST]
[I]Substitute[/I] equation (1) into equation (2) for p:
1.35h + 0.75(h + 40) = 292.50
1.35h + 0.75h + 30 = 292.50
2.10h + 30 = 292.50
To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.10h%2B30%3D292.50&pl=Solve']plug this equation into our search engine[/URL] and we get:
h = 125
The problem asks for number of pizza slices sold (p). So we substitute our value above of h = 125 into equation (1):
p = 125 + 40
p = [B]165[/B]

At Appliance Market, a salesperson sells a dishwasher for $569. She gets a commission rate of 18 per

At Appliance Market, a salesperson sells a dishwasher for $569. She gets a commission rate of 18 percent. Which expression represents how much she will receive in commission from the sale?
Since 18 percent = 0.18, we have:
Commission = Sales * Commission Percent
Commission = 569 * 0.18
Commission = [B]$102.42[/B]

At Billy’s Baseball Dugout, they are having a sale on merchandise. All bats cost $45.00, sunflower s

At Billy’s Baseball Dugout, they are having a sale on merchandise. All bats cost $45.00, sunflower seeds, $1.50, and cleats $85.00. Write an expression if you bought b bats, s sunflower seeds, and c cleats.
Since amount = cost * quantity, we have a cost of:
[B]45b + 1.50s + 85c[/B]

Belle bought 30 pencils for $1560. She made a profit of $180. How much profit did she make on each p

Belle bought 30 pencils for $1560. She made a profit of $180. How much profit did she make on each pencil
The cost per pencil is:
1560/30 = 52
Build revenue function:
Revenue = Number of Pencils * Sales Price (s)
Revenue = 30s
The profit equation is:
Profit = Revenue - Cost
Given profit is 180 and cost is 1560, we have:
30s - 1560 = 180
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=30s-1560%3D180&pl=Solve']type this equation into our search engine[/URL] and we get:
s = 58
This is sales for total profit. The question asks profit per pencil.
Profit per pencil = Revenue per pencil - Cost per pencil
Profit per pencil = 58 - 52
Profit per pencil = [B]6[/B]

Blanca works as a salesperson and earns a base salary of $72 per week plus a commission of 12% of al

Blanca works as a salesperson and earns a base salary of $72 per week plus a commission of 12% of all her sales. If Blanca had $75 in weekly sales, how much did she make?
[U]Find the commission on her sales[/U]
Commission = Sales * 12%
Commission = 75 * 0.12 = 9
[U]Now add in her base salary[/U]
Total Salary = Base Salary + Commission
Total Salary = 72 + 9
Total Salary = [B]81[/B]

Bond Yield Rates

Calculates the yield rate of bonds using the Yield Approximation Method or the Bond Salesman Method.

Brendan bought an aquarium originally priced at $50 but on sale for 50% off. After 12% sales tax, wh

Brendan bought an aquarium originally priced at $50 but on sale for 50% off. After 12% sales tax, what was the total cost?
50% off of 50 means they pay half, or 1/2(50) = 25.
Now, this gets taxed at 12%. So we multiply 25 * 1.12
Total Cost = 25(1.12)
Total Cost = [B]$28[/B]

Carol bought a pair of jeans for $12.95 and a belt for $3.79. The sales tax is $1.01. Carol gave the

Carol bought a pair of jeans for $12.95 and a belt for $3.79. The sales tax is $1.01. Carol gave the store clerk a $20.00 bill. How much change should she get back?
Calculate total cost:
Total cost = Jeans + Belt + Sales Tax
Total cost = $12.95 + $3.79 + $1.01
Total cost = $17.75
Calculate Change
Change = Carol's payment - Total cost
Change = $20 - $17.75
Change = [B]$2.25[/B]

Chicken is on sale for $3.90 per pound. If Ms.Gelllar buys 2.25 pounds of chicken, how much will she

Chicken is on sale for $3.90 per pound. If Ms.Gelllar buys 2.25 pounds of chicken, how much will she spend? round to the nearest penny and show your work
Total spend = Cost per pound * Number of pounds
Total spend = $3.90 * 2.25 pounds
Total spend = [B]$8.78[/B] (rounded to 2 digits)

Cost Recovery Method

Given a sales price, cost, and set of payments, this determines the gross profit per year based on the cost recovery method.

Denise buys a soda for 90 cents, a candy bar for $1.20 and a bag of chips for $2.90. Assuming a 3.5

Denise buys a soda for 90 cents, a candy bar for $1.20 and a bag of chips for $2.90. Assuming a 3.5 percent sales tax, how much change would she receive from a $10 bill
1. Change = $10 - Total Bill
Total Bill = (Soda + Candy Bar + Bag of Chips) * 1.035
Total Bill = ($0.90 + $1.20 + $2.90) * 1.035
Total Bill = $5 * 1.035
2. Total Bill = $5.18
Plug Equation (2) into Equation (1), we have:
Change = $10 - $5.18
Change = [B]$4.82[/B]

Earnings Before Interest and Taxes (EBIT) and Net Income

Given inputs of sales, fixed costs, variable costs, depreciation, and taxes, this will determine EBIT and Net Income and Profit Margin

Emily buys a car for 9000 sells it for 12000. Whats the profit?

Emily buys a car for 9000 sells it for 12000. Whats the profit?
Profit = Sale Price - Purchase Price
Profit = 12,000 - 9,000
Profit = [B]3,000[/B]

Find the total coast of four nights lodging at $62.00 per night with 8 1/2% sales tax.

Find the total coast of four nights lodging at $62.00 per night with 8 1/2% sales tax.
[U]Calculate Total lodging cost[/U]
Total lodging cost = Nightly Rate * Number of Nights
Total lodging cost = 62 * 4
Total lodging cost = 248
[U]Calculate total bill with tax[/U]
Total bill with tax = Total bill * (1 + sales tax percent)
Total bill with tax = 248 * (1 + 0.85) <-- 8 1/2% = 0.085 as a decimal
Total bill with tax = 248 * 1.085
Total bill with tax =[B] $269.08[/B]

Francis paid 51.12 for his dinner including tax. The cost of his dinner is 48. What percent is the t

Francis paid 51.12 for his dinner including tax. The cost of his dinner is 48. What percent is the tax?
Answer: [B]6.5%[/B] using our [URL='http://www.mathcelebrity.com/tax.php?p=48&tb=51.12&pl=Calculate+Tax']sales tax calculator[/URL].

Geocache puzzle help

In the first hour, he sold one-half of his sticks, plus one-half of a stick. The next hour, he sold one-third of his remaining sticks plus one-third of a stick. In the third hour, he sold one-fourth of what he had left, plus three-fourths of a stick. The last hour, he sold one-fifth of the remaining sticks, plus one-fifth of a stick. He did not cut up any sticks to make these sales. He returned home with 19 sticks. How many did he originally take to the event?

Geocache puzzle help

Let me post the whole equation paragraph:
Brainteaser # 1: Answer for ACH
A fellow geocacher decided that he would try to sell some hand-made walking sticks at the local geocaching picnic event. In the first hour, he sold one-half of his sticks, plus one-half of a stick. The next hour, he sold one-third of his remaining sticks plus one-third of a stick. In the third hour, he sold one-fourth of what he had left, plus three-fourths of a stick. The last hour, he sold one-fifth of the remaining sticks, plus one-fifth of a stick. He did not cut up any sticks to make these sales. He returned home with 19 sticks. How many did he originally take to the event? Multiply the answer by 3 and reverse the digits. This will give you the answer for ACH in the coordinates. Make sure to multiply and reverse the digits.
What would the answer be?

Google Digital Sales Exam

Exam answers and Study Guide for the Google Digital Sales Exam

Harjap is a salesperson at an electronic store earning a base salary of $420 per week. She also earn

Harjap is a salesperson at an electronic store earning a base salary of $420 per week. She also earns 2.0% commission on sales each month. This month she had $131600 in sales. What was harjaps gross income for this month?
[U]Calculate Monthly Gross Income:[/U]
Gross Income = Monthly Base Salary + Commissions
[U]Calculate Monthly Base Salary:[/U]
Monthly Base Salary = Weekly Base Salary * 4
Monthly Base Salary = $420 * 4
Monthly Base Salary = $1,680
[U]Calculate Commissions:[/U]
Commissions = Sales * Commission Percent
Commissions = $131,600 * 2%
Since 2% as a decimal is 0.02, we have:
Commissions = $131,600 * 0.02
Commissions = $2,632
[U]Calculate Monthly Gross Income:[/U]
Gross Income = Monthly Base Salary + Commissions
Gross Income = $1,680 + $2632
Gross Income = [B]$4,312[/B]

Hope it's okay to ask this here?

A candy vendor analyzes his sales records and ?nds that if he sells x candy bars in one day, his pro?t(in dollars) is given byP(x) = ? 0.001x2 + 3x ? 1800
(a.) Explain the signi?cance of the number 1800 to the vendor.
(b.) What is the maximum pro?t he can make in one day, and how many candy bars must he sell to
achieve it?
I got 1800 as the amount he starts with, and can't go over. maximum pro?t as 4950
and if I got that right I am getting stuck on how to find how many candy bars.
Thanks

HubSpot Inbound Sales Exam

Exam answers and Study Guide for the HubSpot Inbound Sales Certification Exam

Hubspot Sales Enablement Exam

Exam answers and Study Guide for the Hubspot Sales Enablement Exam

HubSpot Sales Software Exam

Exam answers and Study Guide for the HubSpot Sales Software Certification Exam

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 ballons are on sale at 15 for$3, whats the cost for a ballon? a)50cents b)25cost c)20cents d)20 d

if ballons are on sale at 15 for$3, whats the cost for a ballon? a)50cents b)25cost c)20cents d)20 dollars
Let c be the cost of 1 balloon. We set up a proportion of balloons to cost:
15/3 = 1/c
To solve this proportion for c, we [URL='https://www.mathcelebrity.com/prop.php?num1=15&num2=1&den1=3&den2=c&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
c = [B]0.2 or 20 cents[/B]

If sales tax is currently 8.2%, write an algebraic expression representing the amount of sales tax y

If sales tax is currently 8.2%, write an algebraic expression representing the amount of sales tax you would have to pay for an item that costs D dollars.
8.2% is 0.082 as a decimal. So we have:
Sales Tax Paid = [B]0.082D[/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]

Installment Sales Method of Accounting

Given a sales price, cost amount, installment payment amount and term, this will show the accounting for the Installment Payment method.

Isabel is making face mask. She spends $50 on supplies and plans on selling them for $4 per mask. Ho

Isabel is making face mask. She spends $50 on supplies and plans on selling them for $4 per mask. How many mask does have to make in order to make a profit equal to $90?
[U]Set up the cost function C(m) where m is the number of masks:[/U]
C(m) = supply cost
C(m) = 50
[U]Set up the cost function R(m) where m is the number of masks:[/U]
R(m) = Sale Price * m
R(m) = 4m
[U]Set up the profit function P(m) where m is the number of masks:[/U]
P(m) = R(m) - C(m)
P(m) = 4m - 50
The problems asks for profit of 90, so we set P(m) = 90:
4m - 50 = 90
To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=4m-50%3D90&pl=Solve']type it in our search engine[/URL] and we get:
m = [B]35[/B]

Jake earns 25% commission selling ice cream. How much does he earn for each days sale? a) Friday $10

Jake earns 25% commission selling ice cream. How much does he earn for each days sale?
[LIST]
[*]a) Friday $100
[*]b) Saturday $180
[/LIST]
Commission = Sales * Commission Percent
[U]Calculate part a:[/U]
Commission = 100 * 25%
Commission = [B]$25[/B]
[U]Calculate part b:[/U]
Commission = 180 * 25%
Commission = [B]$45[/B]

Jay purchased tickets for a concert. To place the order, a handling charge of $7 per ticket was cha

Jay purchased tickets for a concert. To place the order, a handling charge of $7 per ticket was charged. A sales tax of 4% was also charged on the ticket price and the handling charges. If the total charge for four tickets was $407.68, what was the ticket price? Round to the nearest dollar.
with a ticket price of t, we have the total cost written as:
1.04 * (7*4 + 4t)= 407.68
Divide each side by 1.04
1.04 * (7*4 + 4t)/1.04= 407.68/1.04
Cancel the 1.04 on the left side and we get:
7*4 + 4t = 392
28 + 4t = 392
To solve this equation for t, we [URL='https://www.mathcelebrity.com/1unk.php?num=28%2B4t%3D392&pl=Solve']type it in our math engine[/URL] and we get:
t = [B]91[/B]

Jennifer spent $11.25 on ingredients for cookies shes making for the school bake sale. How many cook

Jennifer spent $11.25 on ingredients for cookies shes making for the school bake sale. How many cookies must she sale at $0.35 apiece to make profit?
Let x be the number of cookies she makes. To break even, she must sell:
0.35x = 11.25
Use our [URL='http://www.mathcelebrity.com/1unk.php?num=0.35x%3D11.25&pl=Solve']equation calculator[/URL], and we get:
x = 32.14
This means she must sell [B]33[/B] cookies to make a profit.

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]

Joe worked in a shoe department where he earned $325 weekly and 6.5% commission on all of his sales.

Joe worked in a shoe department where he earned $325 weekly and 6.5% commission on all of his sales. What was joe’s total sales if he earned $507 last week
Let s be total Sales. 6.5% is 0.065 as a decimal, so Joe's earnings are given by:
0.065s + 325 = 507
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.065s%2B325%3D507&pl=Solve']type this equation into our math engine[/URL] and we get:
s = [B]2800[/B]

John bought a painting for $600 and sold it for $648. Find the profit as a percentage of the cost.

John bought a painting for $600 and sold it for $648. Find the profit as a percentage of the cost.
[U]Calculate the profit:[/U]
Profit = Sale Price - Purchase price
Profit = 648 - 600
Profit = 48
[U]Calculate Profit percentage of cost =[/U]
Profit percentage of cost = 100% * Profit/cost
Profit percentage of cost = 100% * 48 / 600
Profit percentage of cost = [B]8%[/B]

John is paid a retainer of $550 a week as well as a 2% commission on sales made. Find his income for

John is paid a retainer of $550 a week as well as a 2% commission on sales made. Find his income for the week if in one week he sells cars worth of $80000
Set up the income function C(s) where s is the number of sales for a week. Since 2% can be written as 0.02, we have:
I(s) = Retainer + 2% of sales
I(s) = 550 + 0.02s
The problem asks for a I(s) where s = 80,000:
I(s) = 550 + 0.02(80000)
I(s) = 550 + 1600
I(s) = [B]2150[/B]

Jonathan earns a base salary of $1500 plus 10% of his sales each month. Raymond earns $1200 plus 15%

Jonathan earns a base salary of $1500 plus 10% of his sales each month. Raymond earns $1200 plus 15% of his sales each month. How much will Jonathan and Raymond have to sell in order to earn the same amount each month?
[U]Step 1: Set up Jonathan's sales equation S(m) where m is the amount of sales made each month:[/U]
S(m) = Commission percentage * m + Base Salary
10% written as a decimal is 0.1. We want decimals to solve equations easier.
S(m) = 0.1m + 1500
[U]Step 2: Set up Raymond's sales equation S(m) where m is the amount of sales made each month:[/U]
S(m) = Commission percentage * m + Base Salary
15% written as a decimal is 0.15. We want decimals to solve equations easier.
S(m) = 0.15m + 1200
[U]The question asks what is m when both S(m)'s equal each other[/U]:
The phrase [I]earn the same amount [/I]means we set Jonathan's and Raymond's sales equations equal to each other
0.1m + 1500 = 0.15m + 1200
We want to isolate m terms on one side of the equation.
Subtract 1200 from each side:
0.1m + 1500 - 1200 = 0.15m + 1200 - 1200
Cancel the 1200's on the right side and we get:
0.1m - 300 = 0.15m
Next, we subtract 0.1m from each side of the equation to isolate m
0.1m - 0.1m + 300 = 0.15m - 0.1m
Cancel the 0.1m terms on the left side and we get:
300 = 0.05m
Flip the statement since it's an equal sign to get the variable on the left side:
0.05m = 300
To solve for m, we divide each side of the equation by 0.05:
0.05m/0.05 = 300/0.05
Cancelling the 0.05 on the left side, we get:
m = [B]6000[/B]

Jose bought a shirt for $25.00. The sales tax was 8%. If Jose paid with $40, what was his change?

Jose bought a shirt for $25.00. The sales tax was 8%. If Jose paid with $40, what was his change?
Total Bill is 25 * 1.08 = $27
Change due = 40 - 27 = $[B]13[/B]

juan sells raffle tickets at a charity event for $6 each.How many tickets does he have to sell to ma

juan sells raffle tickets at a charity event for $6 each.How many tickets does he have to sell to make $144?
Tickets needed = Total Sales / Cost per ticket
Tickets needed = 144/6
Tickets needed = [B]24[/B]

Kaitlin is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the nu

Kaitlin is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of Math is Fun she sells. Suppose that x and y are related by the equation 2500+110x=y. What is Kaitlin totalm pay if she doesnt sell any copies of Math is Fun?
We want the value of y when x = 0.
y = 2500 + 110(o)
y = 2500 + 0
[B]y = 2500[/B]

Local salesman receives a base salary of $650 monthly. He also receives a commission of 11% on all s

Local salesman receives a base salary of $650 monthly. He also receives a commission of 11% on all sales over $1500. How much would he have to sell in one month if he needed to have $3000
Let the Sales amount be s. We have:
Sales over 1,500 is written as s - 1500
11% is also 0.11 as a decimal, so we have:
0.11(s - 1500) + 650 = 3000
Multiply through:
0.11s - 165 + 650 = 3500
0.11s + 485 = 3500
To solve this equation for s, [URL='https://www.mathcelebrity.com/1unk.php?num=0.11s%2B485%3D3500&pl=Solve']we type it in our search engine[/URL] and we get:
s = [B]27,409.10[/B]

Markup Markdown

Given the 3 items of a markup word problem, cost, markup percentage, and sale price, this solves for any one of the three given two of the items. This works as a markup calculator, markdown calculator.

Melinda is paid 17000 per year. She is also paid a sales commission of 5% of the value of her sales.

Melinda is paid 17000 per year. She is also paid a sales commission of 5% of the value of her sales. Last year she sold 344000 worth of products. What percent of her total income was her commission?
Calculate Melinda's commission:
344,000 * 0.05 = 17,200
Calculate her total income for the year
Total Income = Base Pay + Commission
Total Income = 17,000 + 17,200
Total Income = 34,200
Calculate the percent of her income which is commission:
Commission Income Percent = 100 * 17,200/34,200
Commission Income Percent = 100 * 0.5029
[B]Commission Income Percent = 50.29%[/B]

Mike writes a book and gets 15% royalty of total sales. He sells 50,000 books at a cost of $35 per b

Mike writes a book and gets 15% royalty of total sales. He sells 50,000 books at a cost of $35 per book. What is the royalty he receives? Remember to put the $ symbol in your answer. For example, if your answer is 10 dollars, write $10 in the answer box.
[U]Calculate total sales:[/U]
Total Sales = Number of Books * Price per book
Total Sales = 50,000 * $35
Total Sales = $1,750,000
[U]Now calculate Mike's royalties:[/U]
Royalties = Total Sales * Royalty Percent
Royalties = $1,750,000 * 15%
[URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=15&den1=1750000&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Royalties[/URL] = [B]$262,500[/B]

On the first day of ticket sales the school sold 3 senior citizen tickets and 10 child tickets for a

On the first day of ticket sales the school sold 3 senior citizen tickets and 10 child tickets for a total of $82. The school took in $67 on the second day by selling 8 senior citizen tickets And 5 child tickets. What is the price of each ticket?
Let the number of child tickets be c
Let the number of senior citizen tickets be s
We're given two equations:
[LIST=1]
[*]10c + 3s = 82
[*]5c + 8s = 67
[/LIST]
We have a system of simultaneous equations. We can solve it using any one of 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter what method we choose, we get:
[LIST]
[*][B]c = 7[/B]
[*][B]s = 4[/B]
[/LIST]

Out of the 485 Cookies for the bake sale, 2/5 were chocolate chip. Estimate the number of chocolate

Out of the 485 Cookies for the bake sale, 2/5 were chocolate chip. Estimate the number of chocolate chips
We want 2/5 of 485. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=485&frac2=2/5&pl=Multiply']type this in our search engine[/URL] and we get;
[B]194[/B]

Penelope and Owen work at a furniture store. Penelope is paid $215 per week plus 3.5% of her total s

Penelope and Owen work at a furniture store. Penelope is paid $215 per week plus 3.5% of her total sales in dollars, xx, which can be represented by g(x)=215+0.035x. Owen is paid $242 per week plus 2.5% of his total sales in dollars, xx, which can be represented by f(x)=242+0.025x. Determine the value of xx, in dollars, that will make their weekly pay the same.
Set the pay functions of Owen and Penelope equal to each other:
215+0.035x = 242+0.025x
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=215%2B0.035x%3D242%2B0.025x&pl=Solve']equation calculator[/URL], we get:
[B]x = 2700[/B]

Percentage of Completion

Given a sales price, total costs, and costs per period, this determines the gross profit to date using the percentage of completion method.

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.

Rachel works at a bookstore. On Tuesday, she sold twice as many books as she did on Monday. On Wedne

Rachel works at a bookstore. On Tuesday, she sold twice as many books as she did on Monday. On Wednesday, she sold 6 fewer books than she did on Tuesday. During the 3 days Rachel sold 19 books. Create an equation that can be used to find m, a number of books Rachel sold on Monday.
Let me be the number of books Rachel sold on Monday. We're given Tuesday's book sales (t) and Wednesday's books sales (w) as:
[LIST=1]
[*]t = 2m
[*]w = t - 6
[*]m + t + w = 19
[/LIST]
Plug (1) and (2) into (3):
Since t = 2m and w = t - 6 --> 2m - 6, we have:
m + 2m + 2m - 6 = 19
Combine like terms:
5m - 6 = 19
[URL='https://www.mathcelebrity.com/1unk.php?num=5m-6%3D19&pl=Solve']Plugging this equation into our search engine[/URL], we get:
[B]m = 5[/B]

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]

Receivables Ratios

Given Net Sales, Beginning Accounts Receivable, and Ending Accounts Receivable, this determines Average Accounts Receivable, Receivables turnover ratio, and Average Collection Period.

sales 45,000 commission rate is 3.6% and salary is $275

sales 45,000 commission rate is 3.6% and salary is $275
Set up the commission function C(s) where s is the salary:
C(s) = Commission * s + salary
We're given: C(s) = 45,000, commission = 3.6%, which is 0.036 and salary = 275, so we have:
0.036s + 275 = 45000
To solve for s, we type this equation into our search engine and we get:
s = [B]1,242,361.11[/B]

Sales Price Variance

Calculates the Sales Price Variance and Total Variance for a group of products

Sales Tax

Given a sales price and a total bill, this calculates the sales tax amount and sales tax percentage

Sales tax is currently 9.1%. Write an algebraic expression to represent the total amount paid for an

Sales tax is currently 9.1%. Write an algebraic expression to represent the total amount paid for an item that costs d dollars after tax is added to the purchase.
We need to increase the price by 9.1%. Our expression is:
[B]1.091d[/B]

Sales tax is directly proportional to cost. If the sales tax on a 46000 automobile is $240, what is

Sales tax is directly proportional to cost. If the sales tax on a 46000 automobile is $240, what is the sales tax on a $9000 automobile?
Set up a proportion of sales tax to purchase price where s is the sales tax on a 9000 automobile:
240/46000 = s/9000
[URL='https://www.mathcelebrity.com/prop.php?num1=240&num2=s&den1=46000&den2=9000&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our search engine[/URL] and we get:
s = [B]46.96[/B]

Sales Tax Question

Cost of an item is $55 the total cost is $58.30 what is the sales tax rate and amount of tax ?
[URL='http://www.mathcelebrity.com/tax.php?p=55&tb=58.30&pl=Calculate+Tax']Answer[/URL]

Savannah is a salesperson who sells computers at an electronics store. She makes a base pay of $90 e

Savannah is a salesperson who sells computers at an electronics store. She makes a base pay of $90 each day and is also paid a commission for each sale she makes. One day, Savannah sold 4 computers and was paid a total of $100. Write an equation for the function P(x), representing Savannah's total pay on a day on which she sells x computers.
If base pay is $90 per day, then the total commission Savannah made for selling 4 computers is:
Commission = Total Pay - Base Pay
Commission = 100 - 90
Commission = $10
Assuming the commission for each computer is equal, we need to find the commission per computer:
Commission per computer = Total Commission / Number of Computers Sold
Commission per computer = 10/4
Commission per computer = $2.50
Now, we build the Total pay function P(x):
Total Pay = Base Pay + Commission * Number of Computers sold
[B]P(x) = 90 + 2.5x[/B]

Short Sale Yield Rate

Calculates the Yield Rate on a short sale of stock.

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]

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Susan makes and sells purses. The purses cost her $15 each to make, and she sells them for $30 each.

Susan makes and sells purses. The purses cost her $15 each to make, and she sells them for $30 each. This Saturday, she is renting a booth at a craft fair for $50. Write an equation that can be used to find the number of purses Susan must sell to make a profit of $295
Set up the cost function C(p) where p is the number of purses:
C(p) = Cost per purse * p + Booth Rental
C(p) = 15p + 50
Set up the revenue function R(p) where p is the number of purses:
R(p) = Sale price * p
R(p) = 30p
Set up the profit function which is R(p) - C(p) equal to 295
30p - (15p + 50) = 295
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=30p-%2815p%2B50%29%3D295&pl=Solve']we type it into our search engine[/URL] and we get:
p = [B]23[/B]

tammy earns $18000 salary with 4% comission on sales. How much should she sell to earn $55,000 total

tammy earns $18000 salary with 4% comission on sales. How much should she sell to earn $55,000 total
We have a commission equation below:
Sales * Commission percent = Salary
We're given 4% commission percent and 55,000 salary. With 4% as 0.04, we have:
Sales * 0.04 = 55,000
Divide each side of the equation by 0.04, and we get:
Sales = [B]1,375,000[/B]

The basketball team is selling candy as a fundraiser. A regular candy bar cost 0.75 and a king sized

The basketball team is selling candy as a fundraiser. A regular candy bar cost 0.75 and a king sized candy bar costs 1.50. In the first week of the sales the team made 36.00. Exactly 12 regular sized bars were sold that week. How many king size are left?
Let r be the number of regular bars and k be the number of king size bars. Set up our equations:
[LIST=1]
[*]0.75r + 1.5k = 36
[*]r = 12
[/LIST]
[U]Substitute (2) into (1)[/U]
0.75(12) + 1.5k = 36
9 + 1.5k = 36
[U]Use our equation solver, we get:[/U]
[B]k = 18[/B]

The dance committee of pine bluff middle school earns $72 from a bake sale and will earn $4 for each

The dance committee of pine bluff middle school earns $72 from a bake sale and will earn $4 for each ticket sold they sell to the Spring Fling dance. The dance will cost $400
Let t be the number of tickets sold. We have a Revenue function R(t):
R(t) = 4t + 72
We want to know t such that R(t) = 400. So we set R(t) = 400:
4t + 72 = 400
[URL='https://www.mathcelebrity.com/1unk.php?num=4t%2B72%3D400&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]t = 82[/B]

The original price of a computer was $895.00. Eleanor had a 25% off coupon which she was able to us

The original price of a computer was $895.00. Eleanor had a 25% off coupon which she was able to use to make the purchase. If sales tax of 6.5% was added after the discount was taken, how much did Eleanor pay altogether for the computer?
First, apply the discount:
$895 * 25% = $223.75
$895 - $223.75 = $671.25
Now, apply sales tax of 6.5% to this discount price of $671.25
$671.25 * 1.065 = [B]$714.88[/B]

the price of a remote control helicopeter is $34.40. a remote control boat costs 4/5 the price of th

the price of a remote control helicopter is $34.40. a remote control boat costs 4/5 the price of the helicopter. sales tax on the remote control boat is 8%.what is the price of the remote control boat, including sales tax? round your answer to the nearest penny
4/5 of 34.40 = $27.52
Add sales tax:
27.52(1.08) = [B]$29.72[/B]

The Radio City Music Hall is selling tickets to Kayla’s premiere at the Rockettes. On the first day

The Radio City Music Hall is selling tickets to Kayla’s premiere at the Rockettes. On the first day of ticket sales they sold 3 senior citizen tickets and 9 child tickets for a total of $75. It took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price of each senior citizen ticket and each child ticket?
Let the cost of child tickets be c
Let the cost of senior tickets be s
Since revenue = cost * quantity, we're given two equations:
[LIST=1]
[*]9c + 3s = 75
[*]5c + 8s = 67
[/LIST]
To solve this simultaneous group of equations, we can use 3 methods:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we use, we get the same answer:
[LIST]
[*][B]c = 7[/B]
[*][B]s = 4[/B]
[/LIST]

The regular price of a shirt was $19.00, but it is on sale for $13.30. What is the percent that the

The regular price of a shirt was $19.00, but it is on sale for $13.30. What is the percent that the shirt has been discounted?
Using our [URL='http://www.mathcelebrity.com/markup.php?p1=19&m=&p2=++13.30&pl=Calculate']markdown calculator[/URL], we get a 30% markdown, or sale.

The sale price of an item that is discounted by 20% of its list price L

The sale price of an item that is discounted by 20% of its list price L
S = L - 20%/100 * L
S = L - 0.20L
[B]S = 0.8L[/B]

The sales price of a new compact disc player is $210 at a local discount store. At the store where t

The sales price of a new compact disc player is $210 at a local discount store. At the store where the sale is going on, each new cd is on sale for $11. If Kyle purchases a player and some cds for $243 how many cds did he purchase?
If Kyle bought the player, he has 243 - 210 = 33 left over.
Each cd is 11, so set up an equation to see how many CDs he bought:
11x = 33
Divide each side by 11
[B]x = 3[/B]

The sales price s of a pair of shoes plus 4% sales tax

The sales price s of a pair of shoes plus 4% sales tax
Total price is s(1 + 0.04) or [B]s(1.04)[/B]

The sales tax for an item was $21.50 and it cost $430 before tax. Find the sales tax rate. Write you

The sales tax for an item was $21.50 and it cost $430 before tax. Find the sales tax rate. Write your answer as a percentage.
Sales tax percentage is:
21.50/430 = 0.05
To get a percentage, multiply the decimal by 100
0.05 * 100 = [B]5%[/B]

The sales tax rate in a city is 7.27%. How much sales tax is charged on a purchase of 5 headphones

The sales tax rate in a city is 7.27%. How much sales tax is charged on a purchase of 5 headphones at $47.44 each? What is the total price?
[U]First, calculate the pre-tax price:[/U]
Pre-tax price = Price per headphone * Number of Headphones
Pre-tax price = $47.44 * 5
Pre-tax price = $237.20
Now calculate the tax amount:
Tax Amount = Pre-Tax Price * (Tax Rate / 100)
Tax Amount = $237.20 * 7.27/100
Tax Amount = $237.20 * 0.0727
Tax Amount = [B]$17.24
[/B]
Calculate the total price:
Total Price = Pre-Tax price + Tax Amount
Total Price = $237.20 + $17.24
Total Price = [B]$254.44[/B]

The school yearbook costs $15 per book to produce with an overhead of $5500. The yearbook sells for

The school yearbook costs $15 per book to produce with an overhead of $5500. The yearbook sells for $40. Write a cost and revenue function and determine the break-even point.
[U]Calculate cost function C(b) with b as the number of books:[/U]
C(b) = Cost per book * b + Overhead
[B]C(b) = 15b + 5500[/B]
[U]Calculate Revenue Function R(b) with b as the number of books:[/U]
R(b) = Sales Price per book * b
[B]R(b) = 40b[/B]
[U]Calculate break even function E(b):[/U]
Break-even Point = Revenue - Cost
Break-even Point = R(b) - C(b)
Break-even Point = 40b - 15b - 5500
Break-even Point = 25b - 5500
[U]Calculate break even point:[/U]
Break-even point is where E(b) = 0. So we set 25b - 5500 equal to 0
25b - 5500 = 0
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=25b-5500%3D0&pl=Solve']type this equation into our search engine[/URL] and we get:
[B]b = 220[/B]

There is a sales tax of $15 on an item that costs $153 before tax. A second item costs $81.60 before

There is a sales tax of $15 on an item that costs $153 before tax. A second item costs $81.60 before tax. What is the sales tax on the second item?
We assume the goods are bought in the same store, so tax rates are the same:
Tax Rate = Tax Amount / Cost before tax
Tax Rate = 15/153
Tax Rate = 0.098 or 9.8%
Calculate sales tax on the second item
Sales Tax = Cost before Tax * Tax Rate
Sales Tax = 81.60 * 0.098
Sales Tax = 7.9968
We round to 2 decimals for dollars and cents and we get:
Sales Tax = [B]$8.00[/B]

There is a sales tax of $4 on an item that cost $54 before tax. The sales tax on a second item is $1

There is a sales tax of $4 on an item that cost $54 before tax. The sales tax on a second item is $14. How much does the second item cost before tax?
Sales Tax on First Item = Tax Amount / Before Tax Sale Amount
Sales Tax on First Item = 4/54
Sales Tax on First Item = 0.07407407407
For the second item, let the before tax sale amount be b. We have:
0.07407407407b = 14
To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.07407407407b%3D14&pl=Solve']type it in our search engine[/URL] and we get:
b = [B]189[/B]

There is a sales tax of $5 on an item that costs $51 before tax. A second item costs $173.40 before

There is a sales tax of $5 on an item that costs $51 before tax. A second item costs $173.40 before tax. What is the sales tax on the second item?
Calculate the sales tax percent using the first item:
Sales Tax Decimal = 100% * Sales Tax / Pre-Tax Bill
Sales Tax Decimal = 100% * 5/51
Sales Tax Decimal = 0.098
Calculate the sales tax on the second item:
Sales Tax = Pre-Tax bill * (1 + Sales Tax)
Sales Tax = $173.40 (1 + 0.098)
Sales Taax = $173.40 * 1.098
Sales Tax = [B]$190.39[/B]

Tomás is a salesperson who earns a monthly salary of $2250 plus a 3% commission on the total amount

Tomás is a salesperson who earns a monthly salary of $2250 plus a 3% commission on the total amount of his sales. What were his sales last month if he earned a total of $4500?
Let total sales be s. We're given the following earnings equation:
0.03s + 2250 = 4500
To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.03s%2B2250%3D4500&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]75,000[/B]

Wayne’s widget world sells widgets to stores for $10.20 each (wholesale price). A local store marks

Wayne’s widget world sells widgets to stores for $10.20 each (wholesale price). A local store marks them up $6.79. What is the retail price at this store?
[I]Note: Markup means we add to the wholesale price. [/I]
Calculate Retail Price:
Retail Price = Wholesale Price + Markup Amount
Retail Price = $10.20 + $6.79
Retail Price = [B]$16.99[/B]

You are offered two different sales jobs. The first company offers a straight commission of 6% of th

You are offered two different sales jobs. The first company offers a straight commission of 6% of the sales. The second company offers a salary of $330 per week plus 2% of the sales. How much would you have to sell in a week in order for the straight commission offer to be at least as good?
Let s be the sales and C be the weekly commission for each sales job. We have the following equations:
[LIST=1]
[*]C = 0.06s
[*]C = 330 + 0.02s
[/LIST]
Set them equal to each other:
0.06s = 330 + 0.02s
Subtract 0.02s from each side:
0.04s = 330
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=0.04s%3D330&pl=Solve']equation solver[/URL], we get [B]s = 8,250[/B]

You buy a container of cat litter for $12.25 and a bag of cat food for x dollars. The total purchase

You buy a container of cat litter for $12.25 and a bag of cat food for x dollars. The total purchase is $19.08, which includes 6% sales tax. Write and solve an equation to find the cost of the cat food.
Our purchase includes at cat litter and cat food. Adding those together, we're given:
12.25 + x = 19.08
To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=12.25%2Bx%3D19.08&pl=Solve']we type this equation into our search engine[/URL], and we get:
x = 6.83
Since the cat food includes sales tax, we need to remove the sales tax of 6% to get the original purchase price.
Original purchase price = After tax price / (1 + tax rate)
Original purchase price = 6.83/1.06
Original purchase price = [B]$6.44[/B]

You 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]

Your bill for dinner, including a 7.25% sales tax, was $49.95. You want to leave a 15% tip on the co

Your bill for dinner, including a 7.25% sales tax, was $49.95. You want to leave a 15% tip on the cost of the dinner before the sales tax. Find the amount of the tip to the nearest dollar.
Find the pretax cost:
49.95/1.0725 = 46.57
Now, add 15% tip to the pretax bill:
46.57(1.15) = [B]$53.56[/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]