# 01 QBA BADM 221 BASIC BUSINESS MATH SKILLS AND ALGEBRA REVIEW NOTES

```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 &frac12;% = .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
(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
\$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
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