516. The rate and percentage being given to find

the base.

ORAL

EXERCISES.

1. 18 is 3% of what number?

ANALYSIS. Since 3%, or 18, of a certain number is 18, TOO is }

of 18, or 6, and 100 is 600. Hence 18 is 3% of 600.

10. 121% of 96 is 331% of what number?

517. PRINCIPLE.-The base is as many times the percentage as 100% is times the rate.

centage is, or of the base; hence the base is of the percent

age, and of 144 is 192.

2. $54 are 15% of what?

3. $18.75 are 24% of what?

RULE.-Divide the percentage by the rate. Or, take as

many times the percentage as 100% is times the rate.

FORMULA.-Base Percentage Rate.

14. 25% of 800 bu. is 24% of how many bushels ? 15. A farmer sold 3150 bushels of grain and had 30% of his entire crop left. What was his entire crop?

16. A man drew 25% of his bank deposits, and expended 331% of the money thus drawn in the purchase of a horse worth $250. How much money had he in bank at first?

17. If a man owning 45% of a steamboat sells 16% of his share for $5860, what is the value of the whole boat?

18. If $295.12 are 134% of A's money, and 43% of A's money is 8% of B's, how much more money has A than B?

519. The amount, or the difference, and the rate being given to find the base.

1. What number increased by 25% of itself amounts to 60 ?

ANALYSIS.-Since 60 is the number increased by 25% of itself, it is 185, or of the number; and if of the number is 60, the number itself is 4 times of 60, or 48.

2. What number increased by 81% of itself is 130? 3. $70 are 40% more than what sum?

4. A man sold a saddle for $18, which was 121% more than it cost him. What did it cost him?

5. A grocer sold flour for $8.40 a barrel, which was 16% more than he paid for it. What did he pay for it?

6. What number diminished by 20% of itself is 40?

ANALYSIS. Since 40 is the number diminished by 20% of itself, it is, or of the number; and if of the number is 40, the number itself is 5 times of 40, or 50.

7. What number diminished by 5% of itself is 38? 8. What sum diminished by 50% of itself is $20.50 ? 9. 68 yd. are 15% less than what number?

10. A tailor, after using 75% of a piece of cloth, had 94 yards left. How many yards in the whole piece? 11. A sells tea at $.90 a pound, which is 10% less than he paid for it. What did he pay for it?

520. 1. What sum increased by 37% of itself is $2055 ?

OPERATION.

1+.37 1.37

$20551.37=$1500

Or,

ANALYSIS.—Since the number is increased 37%, or by .37 of itself, $2055 is 137%, or 1.37 the

18 of $2055=$2055÷137 × 100-$1500 number. Hence

1.37, is the base or required number. Or,

$2055 divided by

Since $2055, the amount, is 187 of the base, 100 times 17 of $2055, or $1500, is the base.

2. What number increased by 18% of itself equals 2950? 3. What sum increased by 15% of itself is $6900 ?

4. What number diminished by 12% of itself is 2640 ?

5. If the difference is $1000 and the rate 20%, what is the base?

6. What sum diminished by 35% of itself equals $4810?

RULE.-Divide the amount by 1 plus the rate; or, divide the difference by 1 minus the rate.

15. A man sold 160 acres of land for $4563.20, which was 8% less than it cost. What did it cost an acre?

16. A speculator bought 48 bales of cottor, and afterward sold the whole for $2008.80, losing 7%. What was the cost of each bale?

17. A dealer bought a quantity of grain by measure and sold it by weight, thereby gaining 1% in the number of bushels. He sold at 10% above the purchase price, and received $4910.976 for the grain. Required the cost.

18. A merchant, after paying 60% of his debts, found that $3500 would discharge the remainder. What was his whole indebtedness?

19. The net profits of a mill in two years were $6970, and the profits the second year were 5% greater than the profits the first year. What were the profits each year?

20. A man sold two houses at $2500 each; for one he received 20% more than its value and for the other 20% less. Required his loss.

APPLICATIONS OF PERCENTAGE.

521. The applications of percentage are those which are independent of time, as, Profit and Loss, Commission, Stocks, etc.; and those in which time is considered, as, Interest, Discount, Exchange, etc.

Since some one of the four formulas of percentage already considered will apply to any of these applications, the following will serve as a general

RULE. Note what elements of Percentage are given in the problem, and what element is required, and then apply the special rule or formula for the corresponding case.

PROFIT AND LOSS.

522. Profit and Loss are terms used to express the gain or loss in business transactions.

523. Gains and losses are usually estimated at a rate per cent. on the cost, or the money or capital invested.

524. The operations involve the same principles as those of Percentage.

525. The corresponding terms are the following:

1. The Base is the Cost, or capital invested. 2. The Rate is the per cent. of profit or loss.

3. The Percentage is profit or loss.

4. The Amount is the cost plus the profit, or the Selling Price.

5. The Difference, is the cost minus the loss, or the Selling Price.