BASIC BUSINESS MATH REVIEW - NOTES
The following problems and their associated illustrated solutions provide a quick review of basic
business math. Make sure you understand the concepts provided because they are used throughout
the course.
1. How much is 30% of $500?
(.30)(500) = $150
$500 is the total/whole
30% = .30 in decimal format
30% of $500 is
(.30)($500) = $150
2. What is 82.5% of $337.27?
(.825)(337.27) = $278.25
$337.27 is the total/whole
82.5% = 82 ½% = .825 in decimal format
82.5% of $337.27 is
(.825)($337.27) = $278.25
3. How much is 2% of 121?
(.02)(121) = 2.42
121 is the total/whole
2% = .02 in decimal format
2% of 121 is . . .
(.02)(121) = 2.42
4. Add 8.2% to $756.
(1.082)(756) = $817.99
Example One:
$756 is the total/whole
8.2% = .082 in decimal format
8.2% of $756 is
(.082)(756) = $61.99
“ADD” $61.99 to $756
$756 + $61.99 = $817.99
5. Subtract 3% from $287.
Example Two:
$756 is the total/whole
8.2% = .082 in decimal format
100% = 1.00 in decimal format
108.2% = 1.082 in decimal format
108.2% 0f $756 is
(1.082)($756) = $817.99
(.97)(287) = $278.39
Example One:
$287 is the whole/total
3% = .03 in decimal format
3% of 287 is
(.03)($287) = $8.61
“SUBTRACT” $8.61 from $287
$287 - $8.61 = $278.39
Example Two:
$287 is the whole/total
3% = .03 in decimal format
97% = .97 in decimal format
97% of $287 is
(.97)($287) = $278.39
6. What percent is 30 of 50?
30/50 = .60 = 60%
50 is the whole/total
30 is the amount of the whole/total
30 is what percent of the whole (50)
30/50 is
30/50 = .60 or 60%
7. What percent of $121.37 is $36.50? 36.5/121.37 = .3007 or 30.07%
$121.37 is the whole/total
$36.50 is the amount of the whole/total
$36.50 is what percent of the whole ($121.37)
$36.50/$121.37 is
$36.50/$121.37 = .3007 or 30.07%
8. What percent is 60 of 40?
60/40 = 1.5 or 150%
40 is the whole/total
60 is the amount of the whole/total
60 is what percent of the whole (40)
60/40 is
60/40 = 1.5 or 150%
9. If you earn $10,000 in 2006 and $12,000 in 2007, what is the percent change?
Use signed difference/original. +2,000/10,000 = +.20 or +20%
Example One:
$10,000 is what you started with (base)
$12,000 is what you have a year later
$2,000 positive quantitative difference
(The difference between $10,000 and $12,000)
$2,000 difference / what you started with base ($10,000)
$2,000/$10,000 = .20 or 20% . . . . . +.20 or +20% (signs matter)
Example Two:
What you have ($12,000) / by what you started with base ($10,000)
$12,000/$10,000 = 1.20 or 120%
Meaning:$12,000 is 120% of the base or 120% of $10,000
$10,000 = 100%
$12,000 = 120% of the base
Therefore a 20% increase
10. If you earn $120,000 in 2007 and $115,000 in 2008, what is the percent
change?
-5,000/120,000 = -.0417 or -4.17%
Example One:
$120,000 is what you started with (base)
$115,000 is what you have a year later
$5,000 negative quantitative difference
(The difference between $120,000 and $115,000)
$5,000 difference / what you started with base ($120,000)
$2,000/$10,000 = -.0417% or -4.17% (signs matter)
Example Two:
What you have ($115,000) / by what you started with base ($120,000)
$115,000/$120,000 = .9583 or 95.83%
Meaning:$115,000 is 95.83% of the base or 95.83% of $120,000
$120,000 = 100%
$115,000 = 95.83% of the base
Therefore a 4.17% decrease = -4.17%
11. If 14% of a number is 112, what is the number?
.14X = 112, X = 800
14% = .14 in decimal format
X = unknown number or amount
14% of X is 112
.14X = 112
.14X/.14 = 112/.14
X = 800
12. Your salary is $13,500 after receiving an 8% increase, what was your original
salary?
1.08X = 13,500,
X = $12,500
X is your original salary or the unknown
$13,500 is what you have AFTER the increase or raise
Therefore: the $13,500 is 108% of the base or the unknown
108% = 1.08 in decimal format
108% of X(the base) is $13,500
1.08X = $13,500
1.08X/1.08 = $13,500/1.08
X = $12,500
13. After a 24% reduction, the price was $250, what was the original price?
.76X = 250, X = $328.95
X is your original price or the unknown
$250 is the price AFTER the 24% discount
Therefore: the $250 is 76% of the base or original unknown price
76% = .76 in decimal format
76% of X (the base or original price) is $250
.76X = $250
.76X/.76 = $250/.76
X = $328.96
14. A 20% discount amounts to $50
a. What was the original price?
b. What is the new price?
.2X = 50,
X = $250
250 – 50 = $200
X = original price
20% of X is the discount in dollars ($50)
Therefore: 20% of the original price = $50
.20X = $50
.20X/.20 = $50/.20
X = $250 . . . . . Original Price
$250 original price minus $50 discount is new price
$250 - $50 = $200 new price
15. You buy something for $60.00 and want a gross profit of 50% based on cost.
What do you sell it for?
1.5($60) = $90.00
Cost = $60.00
50% of the cost is what you want gross profit to be
50% of $60 = $30, $60 + $30 = $90
Or
Cost = $60.00
100% of cost is cost, 1.00 X $60.00 = $60.00
1.50 = 150%
1.50($60) = $90
Meaning: 100% plus another 50% of the cost was added in one calculation
16. You produce a product for $12.50 and need an 85% gross profit based on cost.
What is the selling price?
1.85($12.50) = $23.13
Cost = $12.50
85% of the cost is what you want gross profit to be
85% of $12.50 = $10.63, $12.50 + $10.63 = $23.13
Or
Cost = $12.50
100% of cost is cost, 1.00 X $12.50 = $12.50
1.85 = 185%
1.85($12.50) = $23.13
Meaning: 100% plus another 85% of the cost was added in one calculation
17. You want to sell a product for $27.99 and make a gross profit on cost of 33 1/3%.
What do you pay for the product? 1.33333C = $27.99, C = $20.99
C = unknown cost
$27.99 = Selling Price (SP)
.33333 = Gross Profit (GP) Based on Cost, 33 1/3% gross profit based on cost
SP will be 100% + 33 1/3% of Cost, 100% of cost = cost, 33 1/3% of cost = gross profit
Therefore: 1.33333C = Selling Price
1.33333C = $27.99
C = $20.99
18. You want to sell a product for $100.00 and you require a 40% gross profit based on Selling
Price. What should you pay for the product?
.60($100.00) = $60.00
Selling Price = 100% = $100.00
Cost of product = 60% of Selling Price
Gross Profit = 40% of Selling Price
Therefore: C = .60($100.00)
C = $60.00
Therefore: GP = .40($100.00) = $40.00
Therefore: C = $100 - $40 = $60.00
19. You want to sell a product for $18.75 and you want a gross profit 15% based on selling
price. What do you pay for the product?
.85($18.75) = $15.94
Selling Price = 100% = $18.75
Cost of product = 85 of Selling Price
Gross Profit = 15% of Selling Price
Therefore: C = .85($18.75)
C = $15.94
Therefore: GP = .15($18.75) = $2.81
Therefore: C = $18.75 - $2.81 = $15.94
20. What is the cost of an item that sells for $49.50 and has a Gross Profit Rate of 45% based
on cost?
1.45C = $49.50, C = $34.14
Selling Price = $49.50
Gross Profit = 45% of Cost
Cost is Unknown = C
Therefore: Cost + Gross Profit = Selling Price
C + .45(C) = $49.50, 1.45C = $49.50, C = $34.14
21. A radio sells for $75.75 and its gross profit rate based on cost is 37%.
What is the Cost?
1.37C = $75.75, C = $55.29
Selling Price = $75.75
Gross Profit = 37% of Cost
Cost is Unknown = C
Therefore: Cost + Gross Profit = Selling Price
C + .37(C) = $75.75, 1.37C = $75.75, C = $55.29
22. A Calculator sells for $100.00 and its cost is $60.00, what is:
The Gross Profit Rate Based on Selling Price?
$40/$100 = .40 = 40%
The Gross Profit Rate based on Cost?
$40/$60 = .66667 = 66.67%
SP – COST = GROSS MARGIN, $100 - $60 = $40 (needed to find the gross margin)
Therefore: based on selling price, GM/SP = $40/$100 = .40 or 40%
Therefore: based on cost, GM/COST = $40/$60 = .66667 = 66.67%
23. The Gross Profit Rate of a Product is 40% of the Selling Price and it amounts to $23.47.
What is the Selling Price?
.40SP = $23.47, SP = $58.67
What is the Cost?
$58.67 - $23.47 = $35.21
Gross Profit Rate is 40% of Selling Price
Gross Profit is $23.47
Therefore: 40% of Selling Price = $23.47, .40SP = $23.47, SP = $58.67
Therefore: Selling Price – Gross Profit = Cost, $58.67 - $23.47 = $35.21
24. The Gross Profit on a coat is $93.25 which is a gross profit rate of 30% based on cost.
What is the Cost?
.30C = $93.25, C = $310.83
What is the Selling Price?
$310.83 + $93.25 = $404.08
Gross Profit Rate is based on Cost
Gross Profit Rate = 30%
Gross Profit is $93.25
Therefore: 30% of the Cost is $93.25, .30C = $93.25, C = $310.83
Therefore: Cost + Gross Margin = Selling Price, $310.83 + $93.25 = $404.08
25. You put $150 dollars in a saving account and at the end of the year you have $163.98.
How much Interest was earned?
$163.98 - $150.00 = $13.98
The beginning amount subtracted from the ending amount will give you interest
Interest Earned when it is an investment (Savings)
Interest Paid when it is a loan, obligation, debt
26. Using the provided information, compute costs.
Variable Cost per Unit = $10X
Fixed Costs in Total = $50,000
If the company makes 10,000 units Variable Cost is:
If the company makes 10,000 units Fixed Cost is:
If the company makes 10,000 units Total Cost is:
$100,000
$ 50,000
$150,000
Y = mx + b, Y = $10(10,000) + $50,000, Y = $150,000.00