2. What is the value of a silver pitcher weighing 2lb. 10 oz. Avoirdupois, at $2.25 per ounce Troy? Ans. $86.13. 3. Which is the heavier, 52§ lb. of lead or 52.625 lb. of silver? Ans. The lead.

4. How many pounds of gold are actually as heavy as 10 lb. of iron ? Ans. 1244 lb.

5. How many times 3 lb. 10 oz. Troy is 5 lb. 12 oz. Avoirdupois? Ans. 1.8229+.

6. A young lady weighs 120 lb. Avoirdupois weight; how much would she weigh by Troy weight? Ans. 145 lb.

7. If a druggist buys 25 lb. Avoirdupois of drugs at $8 a pound, and sells them in prescriptions at the rate of 75 an 3, what is the gain? Ans. $65.10.

COMPARISON OF MONEY.

374. The Pound Sterling is valued at $4.8665; and the Franc at 19.3 cents; the Mark at 23.85 cents.

375. The gold Dollar weighs 25.8 gr.; the silver Dollar, 412 gr.; the Half-dollar, 192.9 gr.; the Sovereign (gold), 123.274 gr.; and the Shilling (silver), 87.27 gr.

1. How many dollars in £25?
2. How many dollars in £14 12s ?
3. How many pounds in $256.16?
4. How many dollars in 240 guineas?
5. How many francs in £42 ?

6. How many pounds in 875 francs ?
7. How many marks in £340?

8. How many pounds in 4375 marks?

An

121.664. Ans. $71.05.

Ans. £52 12s. 9d.—.

Ans. $1226.358. Ans. 1059.03 fr.

Ans. £34 14.03 8.

Ans. 6937.568 marks.

Ans. £214 8s. 3d.-.

9 How many pounds Avoirdupois in 1000 sovereigns?

Ans. 17.6104.

10. An ingot of pure gold was brought from California to be voined at the Philadelphia mint; if it how many gold dollars will it make,

weighed 15 lb. 8 oz. Troy,

of the coin being alloy? Ans. $3886; 7.08 gr. rem.

INTRODUCTION TO PERCENTAGE.

MENTAL EXERCISES.

1. A gain of $2 on $5 is a gain of how many dollars on the hun dred?

SOLUTION.-If the gain on $5 is $2, on $100, which is 20 times $5, the gain is 20 times $2, or $40.

2. A gain of $3 on $5 is a gain of how many dollars on the hundred?

3. What is the gain on a hundred when the gain is 4 on 20? 5 on 20? 4 on 25?

4. If the gain on $100 is $25, what is the gain on $4? on $12? on $20?

5. If the gain on $100 is $20, what is the gain on $5? on $15? on $25?

6. If the gain on $100 is $40, what is the gain on $1? on $12? on $36?

7. If the gain on $100 is $25, what part of the $100 equals the gain? 8. If the gain on $100 is $40, what part of the $100 equals the gain? 9. If the gain on $24 is at the rate of 25 on the 100, what is the gain?

10. If the gain on $25 is at the rate of 20 on the 100, what is the gain?

11. What is the gain on $50 at the rate of 10 on the hundred? 12. What is the gain on $250 at the rate of 20 on the hundred? 13. What is the gain on $360 at the rate of 15 on the hundred? 14. What is the rate per hundred at a gain of $6 on $30?

15. What is the rate per hundred at a gain of $15 on $60?

16. Per cent. means the same as per hundred; what then can we call the rate per hundred?

Ans. Rate per cent.

17. A gain of $20 on $80 is a gain of what per cent.?

18. A loss of $15 on $75 is a loss of what per cent.?

19. What per cent. is a gain of 20 on 40? 5 on 25 4 on 80? 3 on 60? 8 on 200?

20. What is 5 per cent. of 80? 4 per cent. of 24? 20 per cent of 10? 25 per cent. of 48?

SOLUTION.-5 per cent. is at the rate of 5 on the 100, and since 5 is of 100, 5 per cent. of 80 is of 80, which is 4.

21. What is 50 per cent. of 24? 30 per cent. of 60? 40 per cent. of 35? 60 per cent. of 45?

22. What per cent. is a gain of 15 on 60? 18 on 72? 12 on 48? 16 on 80? 20 on 60? 15 on 90?

SECTION VIII.

PERCENTAGE.

376. Percentage is the process of computation in which the basis of comparison is a hundred.

377. The Term per cent.-from per, by, and centum, & hundred-means by or on the hundred; thus, 6 per cent. of any quantity means 6 of every hundred of the quantity.

378. The Symbol of Percentage is %. The per cent. may also be indicated by a common fraction or a decimal; thus 6%==.06.

379. The Quantities considered in percentage are the Base, the Rate, the Percentage, and the Amount or Differ

ence.

380. The Base is the number on which the percentage is computed.

381. The Rate is the number of hundredths of the base which are taken.

382. The Percentage is the result obtained by taking a certain per cent. of the base.

383. The Amount or Difference is the sum or difference of the base and percentage. They may both be embraced under the general term Proceeds.

NOTE.-In computation the rate is usually expressed as a decimal. For the difference between Rate and rate per cent., see Brooks's Philosophy of Arithmetic.

EXPRESSION OF THE RATE.

1. Express 4% as a decimal and common fraction.

SOLUTION.-Since per cent. is so many on a hundred, 4% of a quantity is .04 of it; or, as a common fraction, or of it.

OPERATION.

4%=.04=1.

384. Cases. The subject of percentage is conveniently treated under three distinct cases:

1. Given the rate and base, to find the percentage or pro ceeds.

2. Given the rate and percentage or proceeds, to find the base.

3. Given the base and percentage or proceeds, to find the rate.

NOTE.-Authors usually present the subject in five or six cases, but it is thought that the method here adopted is to be preferred, on account of its logical accuracy and practical convenience.

CASE I.

385. Given, the base and the rate, to find the percentage or the proceeds.

MENTAL EXERCISES.

1. What is 25% of 120 yards?

SOLUTION.-25% of anything is for of it; and of 120 yards is 30 yards. Therefore, etc.

10. Out of a purchase of 120 dozen eggs, 20% turned out to be bad; how many were good?

11. From a hogshead of kerosene containing 108 gallons, 33% leaked out; how many gallons remained?

12. A train of cars running 20 miles an hour, increases its speed 15%; what is the rate of running after the increase?

13. A clerk's salary is $45 a month, but at the beginning of the year it was raised 11%; what did he then receive a month?

14. Mr. Smith paid a tax of 1% on $3000; what was the amount of his tax?

15. In the 10th problem, which is the base, which the rate. and which the percentage?

WRITTEN EXERCISES.

1. What is 6% of $275? What is the amount of $275, increased by 6% of itself?

SOLUTION.-6% of $275 equals .06 times $275, which, by multiplying, we find to be $16.50.

SOLUTION.-A number increased by 6%, or .06 times itself, equals 1.06 times itself; 1.06 times $275 equals $291.50.

OPERATION.

$275

.06

$16.50

OPERATION.

$275

1.06

$291.50

Rule I.-Multiply the base by the rate, to find the per centage.

Rule II.-Multiply the base by 1 plus the rate, to find the amount; or by 1 minus the rate, to find the difference.

NOTES.-1. When the rate gives a small common fraction, take such a part of the base as is indicated by this fraction.

2. The amount equals the base plus the percentage; the difference equals the base minus the percentage.

14. A grain dealer bought 600 bar. of Western flour, and sold 163% of it; how many barrels remained? Ans. 500. 15. A man's income is $1800 a year, of which he pays 12% for house rent; what rent does he pay? Ans. $216. 16. If the bread made from a barrel of flour weighs 33 per cent. more than the flour, what is the weight of the bread? Ans. 261 lb.