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 B Sales tax = 6 1/2 % x $25
Sales tax = $1.63 THE DIFFERENCE BETWEEN PERCENT AND PERCENTAGE
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. The following figure shows a way to remember the formula for computing the percentage. Example: A discount of 23% is offered on a desk costing $374. How much is the discount? The two knowns are the rate, R, which is 23%, and the base, B, $374. The unknown is the percentage, P. The triangle shows the following: P = RB
P = 23% x $374
P = $86.02 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. (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 _________. ANALYZING WORD PROBLEMS ASKING FOR A PERCENTAGE
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? ___________
(b) What is the amount of the discount? ___________ 7. During a 40%-off sale, how much is taken off the price of a snowmobile listed at $795? ____________
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 =