A rule expressed by letters that represent numbers is called a formula. The letters are connected by mathematical symbols that show what is to be done with the numbers.

Thus in the formula B×R=P, the symbol X means that B is to be multiplied by R in order to get P.

Whenever you write the formula BXR=P, think of the words represented by the letters and symbols.

33. Using the percentage formula.

Example 1.- Find P when B = $2785 and R = 5%.

2785 in line 2 is put in place of B, and .05 is put in place of R. This is called substituting their values for the known numbers in the formula. (B and R are the known numbers; P is the unknown number to be found.)

Example 2. Find P when B = $4836 and R=16%. Solution. 1.

2.

3.

Since BXR=P then 4836X=P $806 P

(16%)

EXERCISE 40

Using the form of solution illustrated above, find P:

Using the same form of solution, find the percentage: 11. When the base is $382.75 and the rate is 10%. 12. When the rate is 7% and the base is 194.

13. When the base is 625.8 and the rate is 33%. 14. When the rate is 75% and the base is 38.

15. When the rate is 371% and the base is $4240.

EXERCISE 41

Miscellaneous Review Drill

1. Find the sums of the following columns. Time

7. Repeat Example 6, substituting 121% for 50%.

3. Out of 22 tons of coal on hand on October 1st, a man found that he had used about 70% up to January 1st. How many tons did he have left on January 1st?

9. A certain firm sold $250,000 worth of goods in 1915. In 1918, its sales were 425% of that amount.

its sales in 1918?

What were

10. The average wage earned by the 284 employees of a certain factory was $1375.15 per year. How much did the company pay out in wages during the year?

11. Give the per cent equivalent to:

a. 1, 1, 1, 1, 1, §, 10, 12.

b. 31, 21, 51, 61, 21.

12. How many times a number is:

300% of it? 500% of it? 250% of it? 175% of it?

TABLE A.

EXERCISE 42

THE PANAMA CANAL

Below are the distances from New York City by the former all-water route and by the Panama Canal.

TABLE B. Below are the numbers of vessels of certain nations that passed through the canal.

TABLE C.-Below is given the record of the traffic on the canal during the first half of the year 1917.

1. How much less is the distance via the Panama Canal than by the former water route: a. To San Francisco? b. to Hawaii? c. to Manila?

2. What was the total number of vessels of the nations named that passed through the canal in each year?

3. What was the average weight of cargo in the first half of 1917:

a. From the Atlantic to the Pacific? b. From the Pacific to the Atlantic?

4. What was the average net tonnage per vessel:

a. From the Atlantic to the Pacific?

b. From the Pacific to the Atlantic?

5. If the charge for passage through the canal of a ship with cargo is $1.20 per ton of net tonnage (carrying capacity), what would be the charge for a vessel having the tonnage found in Example 4?

6. If the charge for passage through the canal of a ship without passengers is 40% less than when loaded, as in Example 5, what would be the charge for such a vessel, if the tonnage is that found in Example 4?

V. SOME APPLICATIONS OF PERCENTAGE

34. Application of percentage to increase and de

crease.

By increasing a quantity or number is meant adding to it; by decreasing a quantity or number is meant subtracting from it.

Example 1. How much is 350 increased by 10% of itself?

Solution. 1. This means that 10% of ""itself," that is, 10% of 350, is to be added to 350. 350 is the base. The percentage is the increase.

2. 3.

10% of 350.10×350=35, the increase.

The result = 350+35=385.

Example 2. How much is $275 decreased by 15% of itself?

Solution.

1. This means that 15% of $275 is to be subtracted from $275. The base = $275 and the rate = 15%; the decrease = the percentage.

2.

15% of $275.15×275= $41.25.

$275 .15 *1375