4. A merchant has 40 pounds of tea, worth $1.50 a pound, which he wishes to mix with four other kinds, worth 95, 75, 60, and 40 cents a pound respectively. How much must he take of each of these four kinds, so that the mixture shall be worth 80 cents a pound?

CASE III.

ART. 184. When the whole mixture is to consist of a certain quantity.

1. A merchant has sugar worth 5, 6, 9, and 12 cents a pound;-with a mixture of these he wishes to fill a hogshead that shall contain 220 pounds. How much of each kind must he take, so, that the compound may be worth 8 cents a pound?

22

{Ratio of the sum of the proportionate quantities to

the number given.

EXPLANATION.—The sum of the proportionate quantities, (found by Case 1,) is 10; the whole number of pounds that is to compose the mixture, is 220; therefore, I must take 220 times as much as the sum of these proportionals, which is 22 times each proportionate quantity.

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2. How many gallons of water, brandy, and rum, must be taken, so as to make a mixture of 90 gallons, worth 80 cents a gallon; providing the water is of no value, the brandy being worth $1.20 a gallon, and the rum, 60 cents a gallon?

REMARK.-Archimedes employed the above in detecting the fraud respecting the crown of Hiero, king of Syracuse. The king had ordered a crown of pure gold to be made; but suspecting his artist to have mixed alloy with it, he requested Archimedes to determine the fact without injuring the crown. To do this, Archimedes took a piece of pure gold, and another of alloy, each equal in weight to the crown, placing them respectively in a vessel filled with water and observing the quantity of water expelled by each he readily determined that the crown was composed of gold and alloy; also the exact proportion in which these ingredients were used.

3. Suppose the weight of the crown and of each mass to be 10 pounds; and that being placed in water, the alloy expelled 92 lbs., the gold .52 lbs., and the crown 64 lbs. Of how much gold, and of how much alloy, did the crown consist? Ans. 3 lbs. of alloy, and 7 lbs. of gold.

ART. 185. The term PER CENT. is derived from the Latin words per and centum, which signify, by the hundred. Percent, therefore, is any sum or number on a hundred, whatever be the denomination, Thus, 5 per cent., signifies 5 for every hundred, or 5 hundredths; 8 per cent. signifies 8 for every hundred, or 8 hundredths, &c.

We have already learned that hundredths can be exexpressed either as a common or as a decinal fraction; thus, 5 hundredths=15 .05; 8 hundredths==.08, &c. In all our calculations in percentage, the rate per cent. is written in the decimal form.

ART. 186. Percentage is extensively used in mercantile transactions, and more or less in the transactions of all other kinds of business; such as Assessment of Taxes, Insurance, Duties, Profit and Loss, Interest, Discount, &c., &c.

ART. 187. Finding the percentage on any sum or quantity.

1. What is 5 per cent. of 225 barrels of sugar?

OPERATION.

225

.05

11.25

=

of the

It may also be solved thus; 5 per cent. is 150 given quantity. Therefore, of 225 barrels = 11-25 barrels, is 5 per cent. of 225 barrels.

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2. What is 6 per cent. of $140 ? 3. What is 8 per cent. of $340 ? 4. What is 35 per cent. of $380 ?

5. What is 47 per cent. of $160·35 ?

6. What is 12 per cent. of 146 yards of cloth ?

7. What is 143 per cent. of 864 gallons of molasses? 8. What is 16 per cent. of 8472 barrels of flour? 9. A man, having $9684, lost by an investment 121 per cent. of it; how much had he remaining ?

10. Bought 24 head of cattle at $25 a head, and sold them, at 25 per cent. advance; how much did I gain?

11. A merchant having $8645, gave 14 per cent. of it for silks; 28 per cent. of it for flour; 43 per cent. of it for broadcloth; and the remainder for sugar. How many dollars did he spend for each?

12. A farmer raising 987 bushels of wheat, gives 9 per cent. of it for gathering it; 10 per cent. of the remainder for thrashing; and 10 per cent. of what now remains for flouring. How much has he remaining?

13. A merchant bought 563 barrels of cider for $2837; and sold 45 per cent. of it, at $6.85 a barrel; 35 per cent. of it, at $7.121 a barrel; and the remainder for what it cost. How much did he gain by the operation?

14. A speculator invested $8640 in a speculation, and lost 25 per cent.; he then invested the remainder in a speculation and gained 15 per cent.; he now invested this amount in speculation and gained 24 per cent. How much did he make by the operation?

INSURANCE.

ART 188. INSURANCE is an agreement by which a

company, or individuals, obligate themselves to make good any loss or damage of property by fire, shipwreck, or other casualties.

The written agreement of indemnity issued by the Insurers, sometimes called the underwriters, to the persons whose property is insured, is called the POLICY.

The insurance is effected in consideration of a sum of money, called a PREMIUM, which is estimated at a certain rate per cent. on the amount insured, and is paid beforehand, to the insurers.

1. If A gets his ship and cargo insured for $86950, from New York to Liverpool, at 2 per cent.; how much will be the amount of the premium?

2. An insurance of $18640 was effected on the ship Baltic, at 2 per cent. How much did the premium amount to?

3. A dwelling, valued at $1485, was insured, at 3 of 1 per cent. How much was the premium?

4. A steamboat, valued at $55016, has an insurance effected on of its value, at 3 per cent. How much is the premium?

5. A gentleman has his dwelling insured for $8640, at 29 cents on $100. What is the premium?

6. A person at the age of 40, effects an insurance on his life for 3 years for the sum of $12800, at the rate of $1.95 on $160 per annum. How much is the annual pre

mium ?

7. An individual, going to California with the intention of returning at the expiration of 3 years, effects an insurance of $9988 on his life, at of of 13 per cent. per annum. How much is the annual premium?

STOCKS, BROKERAGE AND COMMISSION.

ART. 189. STOCKS are government funds, and the capital of incorporated institutions, such as banks, railroad and manufacturing companies, &c. Stocks are divided into shares, usually varying from $50 to $500 each, the market value of which is at times variable.

The par value of a share is its original cost. When it sells for more than its original cost, it is said to be above par, or at an advance; when it sells for less, it is below par, or at a discount.

The rise or fall in stocks is computed at a certain per cent. on the par value of the shares.

ART. 190. BROKERAGE is the percentage paid to brokers, or dealers in stocks, money, bills of credit, and for the transaction of business.

ART. 191. COMMISSION is the percentage paid to agents and commission merchants, for the purchase, sale, or care of property, and for the transaction of other business.

The rate per cent. of Brokerage or Commission, varies in different places, and depends upon the nature of the business transacted.

1. What will $9864 par value of bank stock cost, at 18 per cent. advance ?

REMARK.-Find 18 per. cent. of $9864 and add it to the $9864; the sum will be the amount required.

2. How much must be given for 25 shares in the Hudsoon River Railroad, at 121 per cent. advance, the shares being $340 each?

3. What is the value of 27 shares of canal stock, at 183 per cent. advance, the shares being $150 each?

4. How much will be the cost of 18 shares of bank stock, at 173 per cent. below par, the shares being $240 each?

5. Bought 87 shares of a certain stock, at 131 per cent. below par, and sold the same, at 173 per cent. above par; how much did I gain, the original shares being $184 each?

6. A gentleman paid a broker & of 1 per cent. to invest $84860 in government funds. How much was the brokerage?

7. A lady, having $84847, paid an agent 1 per cent. commission a year, to take care of it for her. To how much did the commission annually amount?

8. An agent sells 8484 barrels of flour, at $5.871 a