**After completing Unit 10, you will be able to:**

*• Use the percentage formula to compute percentage, rate, or base*.

*• * *Apply the percentage formula to business problems*.

The principle Percentage = Rate x Base is used in many business problems. The formula is P = RB.

LetterExplanationP Percentage (portion, part, or share), always withouta percent signR Rate or percent, usually witha percent signB Base, the original amount

Example:What is the sales tax (P) on a purchase of $25 (B) if the rate of sales tax (R) is 6 1/2%?

Solution:P = R x BSales tax = 6 1/2% x $25

Sales tax = $1.63

Sometimes the words "percent" and "percentage" are used interchangeably. In business mathe-matics, percentage, P, is always a number without a percent sign. Rate, R, (percent) is usually a number followed by percent sign.

1. What is the percentage formula? __________

2. Can equations or formulas be turned around--that is, can the left side be switched with the right side? __________

3. Is RB = P the same as P = RB? __________

4. If P and B are known, what is unknown? ________(a)________

Is P an amount or is it a number followed by a %? ________(b)________

Is R an amount or is it a number followed by a %? _________(c)_________

**COMPUTING THE PERCENTAGE**

The percentage formula can be pictured using a triangle as shown at
the top of the next page. The triangle can be used as a memory aid for
all the variations of the percentage formula.

5. Compute the percentage in the following problems. Remember to convert the percent to a fraction or a decimal. If necessary, use the Aliquot Parts Table in Unit 7.P = RBP = 23% x $374

P = $86.02

(a) What is 33 1/3% of $1,710? _________(b) What is 4% of $1,620? _________

(c) 7% of $25,000 is _________.

(d) What is 12 1/2% of $48,016? _________

(e) 1/2% of $100 is _________.

Problems in which the percentage, P, is unknown can be analyzed as follows.

**Problem: **A sale allows 10% off all marked prices. What is the
allowance on an item marked $195?

6. An $80 article is being sold at a 15% discount.

(a) What part of the percentage formula is unknown? ___________7. During a 40%-off sale, how much is taken off the price of a snowmobile listed at $795? ____________(b) What is the amount of the discount? ___________

8. A salary increase of 6 1/2% will take effect next month. How much will an employee's raise be if her present salary if $1,345 per month? _____________

9. How much is the sales tax on a new car selling for $6,340 if the sales tax rate is 6 1/2%? ___________

10. The power commission has authorized an extra charge of 15.5% for electricity to cover increases in fuel costs. How much of a monthly increase is this for a customer whose electricity bills average $140.00 per month? ____________

11. In the problem "What is 10% of $560?", what is the base? ___________

**FINDING THE RATE OF PERCENT**

Note that the percentage formula P = RB can be rewritten as R = | P
B |
. |

(a) R = ___________(b) R is a number followed by ________________.

13. | Using the formula R = | P
B |
, | compute the rate (R) is P is $0.50 and B is $4.50. _______ |

14. A loss of $34 was sustained on the sale of a desk calculator that cost $520. What was the percent of loss? ____________

**ANALYZING PERCENT PROBLEMS STATED IN WORDS**

Problems in which the percent R is unknown can be analyzed as follows.

What percent of 75 is 25?"What percent" is the unknown, R.

"Of" means multiply.

The number following "of" is the base, B, in this case 75.

"Is" means equals.

The number following "is" is the percentage, in this case 25.

(a) Because R is unknown, use the formula ___________.

(b) R = ___________

(a) Because R is unknown, use the formula ___________.17. Analyze the following problem. If a customer obtained a $15 discount on an article marked $50, what was the percent of discount?(b) R = ___________

Analysis:

(a) First, restate the problem. ________________________________18. Solve the following problems.(b) Second, write the equation.

(c) Third, solve the equation. Because R is unknown, which percentage formula should be used? ____________

(d) What is the amount of R? ___________________

(e) Fourth, prove. _______________________________

(a) What percent of 150 is 50? __________(b) What percent of 6 is 1 1/2? ____________

(c) 28 is what percent of 40? ____________

19. Analyze and solve. Kim Borka received a raise in wages of $30 a week. If her wages were $200 a week, what was the percent of increase? _____________________________________________

20. Analyze and solve. A direct mailing company sent out 5,000 sale circulars and received a return of 40. What was the percent of return? ______________________________________________

21. $85 is what percent of $135?

(a) The formula is ______________.22. In analyzing percentage problems, what word does the base amount always follow? ____________(b) The answer, to the nearest whole percent, is ______________.

23. What percent of $735 is $110.25?

(a) Formula: ____________24. What is 20% of 125? Include in your answer the formula used. ___(b) Answer: ____________________

What percent of 16 is 5? Include in your answer the formula used. _______________(b)______________

**FINDING THE BASE**

Note that the formula P = RB can be rewritten as B = P/R.
The following illustrates a way of remembering the formula.

25. Rewrite the formula P = RB to compute the amount of B. __________________

**ANALYZING BASE PROBLEMS STATED IN WORDS**

Assume that May White received a $150 increase in her monthly salary,
which was a 12% increase. Compute her original monthly salary.

26. Which part of the formula in the above problem is an unknown quantity?
_________(a)________

Which formula should be used? __________(b)__________

What was May White's salary before the raise? __________(c)__________

27. Jon Estro received a salary increase of $165, which was a 15% raise. What was his original salary? __________

28. 8% of what amount is 216?

(a) Restate as an equation. ___________29. 1,045 is 22% of what amount?(b) What formula should be used? ___________

(c) Solve the equation. ___________

(d) The answer is ____________________

(a) Restate as an equation. ___________30. To prove the answer to this type of problem, multiply the rate times the answer, which should equal the percentage.(b) Solve the equation. ___________

(c) What is the answer? ___________

Solve and prove the answers to the following problems.

(a) 6 is 3% of what amount? _______________ Prove. __________31. $176 is 200% of what amount? (Convert 200% to 2.00.) ______________________(b) 15% of what amount is $186? ___________ Prove. ___________

(c) $15 is 200% of what amount? ___________ Prove. ___________

(d) 60% of what amount is $2,160? ___________ Prove. ___________

(e) 110% of what amount is $167.20? ___________ Prove. ___________

(f) 2.50 is 1/2% of what amount? ___________ Prove. ___________

32. Solve the following problems.

(a) $20 is 1/2% of what amount? (Convert ~21% to 0.005.) ___________33. $1,800 is 300% of what amount?(b) 500 is 80% of what amount? ____________

$2,100 is 150% of what amount? _______(b)_______

**Business Applications**

Analyze and solve the following problems.

34. The sales tax on an article was $4.83 and the tax rate is 7%. What did the article cost?

(a) Restate the problem. ______________________35. Jack Bader paid $5.82 sales tax on a ski outfit in a city where the local and state sales tax was 6%.(b) Which of P, R, or B is unknown? ___________

(c) Write an equation. ____________________

(d) How much did the article cost? ____________

(a) Restate the problem. ______________________36. Lorri received an additional $54.08 in her salary check, which represented a 10.3% raise.(b) Which of P, R, or B is unknown? ___________

(c) Write an equation. __________________

(d) How much did the ski outfit cost? ___________

(a) Restate the problem.37. $1,600 was received on a $7,200 investment. What was the percent of return?(b) Which of P, R, or B is unknown? ___________

(c) Write an equation. ____________________

(d) What was the amount of her original salary? __________

(a) Restate the problem. ______________________38. Assume that you were to receive an 8% increase in your hourly wage of $12. What would be the amount of increase?(b) Which of P, R, or B is unknown? ___________

(c) Write an equation. ____________

(d) What was the percent of return on the investment? ___________

(a) Restate the problem. ______________________39. Assume that an experienced worker receives 225% of the base weekly wage. As an experienced worker you receive $675 a week. What is the base wage?(b) Which of P, R, or B is unknown? ___________

(c) Write an equation. ____________

(d) What would be the amount of the salary increase? ___________

(a) Restate the problem. ______________________(b) Which of P, R, or B is unknown? ___________

(c) Write an equation. ____________________

(d) What is the base wage? ___________

You have finished Unit 10. Please select one of the choices below.

**CHECKPOINT** for Unit 10