What was the cost of the several articles, and what the amount

What was the cost of the several articles, and what the amount of his bill?

(35.)

ST. LOUIS, Aug. 25th, 1847.

0.62

1.87

James Henry, Esq.

For 15260 lbs. Pork,

What is the amount of cash requisite to balance the account?

SECTION XII.

PERCENTAGE.

ART. 386. The terms Percentage and Per Cent. signify a certain allowance on a hundred; that is, a certain part of a hundred, or simply hundredths. Thus, the expression 6 per cent. signifies 6 hundredths, (180) 7 per cent., 7 hundredths, (10) &c., of the number, or sum of money under consideration.

Note.-The terms Percentage and Per Cent. are derived from the Latin per and centum, signifying by the hundred.

387. We have seen that hundredths are decimal expressions, occupying the first two places of figures on the right of the decimal point. (Arts. 311, 314.) Now, since percentage and per cent. signify hundredths, it is manifest that they can be expressed by decimals, as in the following

OBS. 1. It will be seen from the preceding Table, that when the given per cent. is less than 10, a cipher must be prefixed to the figure expressing it, in the same manner as when the number of cents is less than 10. (Art. 369. Obs. 1.)

QUEST.-386. What do the terms percentage and per cent. signify? What is meant by 6 per cent., 7 per cent., &c., of any number, or sum?

When the given per cent. is more than 100, it must plainly require a mixed number to express it. (Art. 315. Obs. 2.)

2. Parts of 1 per cent. may be expressed either by a common fraction, or by decimals. Thus, the expression 17 per cent., is equivalent to .17625 per cent. 3. The first two decimal figures properly denote the per cent., for they are hundredths; the other decimals being parts of hundredths, express parts of 1 per cent.

EXAMPLES.

1. Write 1 per cent., 2 per cent., 4 per cent., 6 per cent., 7 per cent., 8 per cent., in decimals.

2. Write 11 per cent.; 12; 14; 15; 16; 23; 65; 93.

3. Write per ct.; 1; 1; † ; 4; 2; 1; 1; 3; §; 1 ; † ; 7; 1. 4. Write 4 per ct.; 64; 71; 91; 121; 161; 115; 4001. 5. An agent collected $700 for a merchant, and received 5 per cent. for his services: how much did he receive?

Analysis. Since 5 per cent. is the same as 15, the agent must have received 15 of $700. Now Too of $700 is $188, which is equal to $7; and 5 hundredths is 5 times $7, or $35.

Operation. $700

.05

$35.00 Ans.

Since .05, we multiply the given number of dollars by .05, and it gives the answer in cents, which we reduce to dollars by pointing off 2 decimals. (Art. 372.) Hence,

388. To calculate percentage on any number, or sum of money.

Multiply the given number or sum by the given per cent. expressed decimally; and point off the product as in multiplication of decimal fractions. (Art. 324.)

OBS. 1. It is important for the learner to observe, that the amount of money collected, is made the basis upon which the percentage is computed. That is, the agent is entitled to 3 dollars, as often as he collects 100 dollars, and not as often as he pays over 100 dollars, as is frequently supposed. For in the latter case he would receive only, instead of of the sum in question. This distinction is important, especially in calculating percentage on large sums.

QUEST.-387. How may per centage or per cent. be expressed? Obs. When the given per cent. is less than 10, how is it written? When more than 100, how? 388. How is percentage calculated? Obs. In collecting money, upon what basis is the per cent. cal culated? If the per cent. contains a common fraction which cannot be expressed decimally, how proceed?

2. Hence, if the per cent. contains a common fraction which cannot be expressed decimally, first multiply by the decimal, then by the common fraction of the given per cent., and point off the sum of their products as above.

6. What is 4 per cent, of $300?

Solution.-Expressed decimally, 43 per cent.-.042; (Art. 387. Obs. 2;) and $300.042=$12.60. Ans.

7. What is 3 per cent. of $256.25 ? 8. What is 2 per cent. of $437.63 ? 9. What is 4 per cent. of $173.04? 10. What is 6 per cent. of $145.13 ? 11. What is 7 per cent. of $1630.10?

12. A man borrowed $150, and paid 7 per cent. for the use of it: how much did he pay ?

13. A merchant bought goods amounting to $1825, and sold them so that he gained 12 per cent.: how much did he gain?

14. A constable collected $862.56, and charged 5 per cent. for his services: how much did he receive; and how much did he pay over?

15. What is 10 per cent. of $4020.50 ?

16. What is 8 per cent. of $1675?

21. What is 83 per cent. of $100.25?

22. A farmer having 1500 sheep, lost 25 per cent. of them: how many did he lose?

23. A merchant having $1960 on deposit, drew out 20 per cent. of it: how much had he left in the bank?

24. A merchant imported 1500 boxes of oranges, and 12 per cent. of them decayed: how many boxes did he lose; and how many had he left?

25. What is per cent. of $1625 ?

28. What is 4 per cent. of $2526.40?

32. A merchant bought a stock of goods amounting to $4565, and paid 3 per cent. for freight: what was the whole cost of his goods?

33. A man's salary is $2000 a year, and he lays up 37 per cent. of it: how much does he spend ?

34. A youth who inherited $20000, spent 40 per cent. of it in dissipation: how much had he left?

35. Two merchants embarked in business with $18250 capital apiece; one gained 20 per cent. and the other lost 20 per cent. the first year: what was then the amount of each man's property?

36. Two men invested $10000 apiece in stocks; one lost 8 per cent., the other 6 per cent.: what was the difference of their loss? 37. What is the difference between 6 per cent. of $1040, and per cent. of $905 ?

7

APPLICATIONS OF PERCENTAGE.

389. PERCENTAGE, or the method of reckoning by hundredths, is applied to various calculations in the practical concerns of life. Among the most important of these are Commission, Brokerage, the Rise and Fall of Stocks, Interest, Discount, Insurance, Profit and Loss, Duties, and Taxes. Its principles, therefore, should be thoroughly understood by every scholar.

COMMISSION, BROKERAGE, AND STOCKS.

390. Commission is the per cent. or sum charged by agents for their services in buying and selling goods, or transacting other

business.

OBS. An Agent who buys and sells goods for another, is called a Commis sion Merchant, a Factor, or Correspondent.

391. Brokerage is the per cent. or sum charged by money dealers, called Brokers, for negotiating Bills of Exchange, and other monetary operations, and is of the same nature as Commission.

QUEST.-399. What is commission ? Obs. What is an agent who buys and sells good for another usually called?