132.

ARBITRATION OF EXCHANGE. CHAIN RULE.

1. If one barrel of flour is worth 4 barrels of apples, and 2 barrels of apples are worth 8 bushels of corn, and 5 bushels of corn are worth 6 bushels of potatoes, and one bushel of potatoes is worth 50 cents, how many barrels of flour will $25 buy? How much are 4 barrels of flour worth?

Questions like the above may be readily solved by the rule of cause and effect, (Art. 131,) by placing each effect opposite to its cause, and making each effect of the same denomination with the next cause.

NOTE. The first numbers in each part of the question are called antecedents, and may be regarded as causes; the following ones are called consequents, and may be regarded as effects.

$51.92=228 barrels, the answer.

In the first question, viz., how many barrels of flour will $25 buy, the unknown quantity is an effect or consequent; the blank is therefore in the column of consequents, the numbers in which are factors of the divisor; the antecedents being factors of the dividend.

In the second question, viz., how much are 4 barrels of flour worth, the unknown quantity is a cause or antecedent; the blank is therefore in the column of antecedents, the numbers in which are factors of the divisor; the consequents being factors of the dividend.

2. If 10 barrels of flour can be bought for 54 bushels of wheat, and 9 bushels of wheat for 20 bushels of corn, and 12 bushels of corn for 10 bushels of rye, and 5 bushels of rye for $3.50, how many barrels of flour can be bought for $50? How much are 18 barrels worth?

NOTE. Cancel equal factors before multiplying.

3. If 15 oranges are worth 35 lemons, and 7 lemons are worth 12 apples, and 18 apples are worth 10 pears, and 8 pears are worth 15 peaches, and 3 peaches are worth 2 cents, what are 10 oranges worth? How many oranges will 40 cents buy?

Debts due in foreign countries are often paid through the medium of a number of persons residing in different countries. The method of changing the currency of one country into that of another, through the medium of one or more intervening currencies, is called Arbitration of Exchange.

The method of operation is the same as for the above questions.

4. If 1 French crown is equal to 80 pence of Holland, and 40 pence of Holland to 24 pence of England, and 20 pence of England to 35 pence of Hamburg, and 60 pence of Hamburg to 1 florin of Frankfort, how many florins of Frankfort are equal to 100 French crowns?

5. A merchant in New York wishes to pay £1000 in London; how many dollars will pay the amount, if he sends his money to Paris at 5 francs 15 centimes to the dollar, and thence to London at 25 francs 80 centimes for £1?

6. Which is best for the merchant, to buy a bill on London, exchange being at a premium of 93 per cent., (122,) to pay the debt named in the last question, or to remit his money through Paris, as there proposed? How many dollars is the difference?

NOTE. The questions in Art. 128 to 132 should be performed by Analysis, as well as by the specific rules given for solving them.

QUESTIONS. What is ratio, and what does it express? Give an example. What are the terms of a ratio? What is the first term called? the second? How is the ratio of one quantity to another obtained? How is ratio expressed? Give examples. What must be

done if the terms are not in the same denomination? How may a ratio be reduced to its lowest terms?

What is a proportion? When do four numbers form a proportion? In what different ways may a proportion be expressed? Which terms of a proportion are called extremes? Which are called means? What products are always equal to each other? To what is either mean equal? To what is either extreme equal? Why? What are given and what is required in questions in simple proportion? Which terms must be of the same kind? When must the second term be greater than the first? When less? Repeat the rule for simple proportion.

What is a compound ratio? How may a compound ratio be reduced to the form of a simple ratio?

What is compound proportion? How may a compound proportion be reduced to the form of a simple proportion? In what terms may equal factors be cancelled? What are given and what is required in questions in compound proportion? What is the rule for compound proportion?

Give

Into what may the terms of a proportion be distinguished? examples. In statements by cause and effect, what products are always equal? How do we write down the terms in solving questions by this method? Which column of numbers constitutes the divisor? Which the dividend? What may be done if any of the terms are fractions or mixed numbers? Which terms should be written first? What terms are causes?

What are effects?

How are debts due in foreign countries often paid? What is meant by arbitration of exchange? How may questions in arbitration of exchange be solved? Of what denomination should each effect be?

133. PARTNERSHIP.

Sometimes two or more persons unite together for the transaction of business. Such a union is termed a partnership. The association thus formed is called a firm, or house. The money or capital employed is called capital, or stock. The process by which partners divide their gain or loss is sometimes called fellowship.

1. A and B form a partnership. A furnishes $300 of the stock, and B $500; they gain $80. How shall the gain be divided between them?

It is evident that they should share the gain in proportion to the stock each furnished; therefore, as A furnished of the stock, he should have of the gain; and as B furnishéd g of the stock, he should have of the gain.

2. Three men hire a pasture for $48. A pastures 4, B 5, and C 3 horses. What part of the whole stock did each furnish? What must each pay?

3. A, B and C formed a partnership. A furnished $450, B $500, and C $600. What part of the whole stock did each furnish? They gained $248. What part of the gain belongs to each? How many dollars? If they lose $93, what part of the loss must each sustain? How many dollars?

4. A bankrupt owes $980; viz., to A $420, to B $350, and to C $210. What part of his effects must each receive? How many dollars should each receive if the bankrupt is worth $840? How much if he is worth $280?

RULE BY PROPORTION. As the whole stock is to each man's stock, so is the whole sum to be divided to each man's share of it.

NOTE. Perform all the examples in this Art. both by Analysis and Proportion.

5. A, B, C, and D send a vessel to the West Indies. A furnishes $1600 of the cargo, B $1800, C $2550, and D $1200. They gain $2288. What per cent. of the money invested do they gain? How many dollars of the gain belong to each?

6. Divide $850 among 5 men, so that their shares shall be in the proportion of 6, 5, 4, 3, and 2, respectively, (that is, so that the first shall have 6 as often as the second has 5, &c.) What is the share of each?

7. Divide $75 between 2 persons, so that A shall have $1 as often as B has $1.

NOTE. A has as often as B has . Their shares are therefore as the numbers 2 and 3.

8. Divide $345 between 3 persons, in the proportions of }, and.

9. Divide $750 among 4 men, in shares which are in the proportion of, 2, ‡, and §.

10. A and B hire a pasture, for which they pay $20. A's horse was in the pasture 13 weeks, and B's 15 weeks. What proportion of the whole should each pay? How many dollars?

11. A bankrupt is worth $10,000; his debts amount to $12,500. How much shall a creditor receive to whom he

owes $500 ?

12. A bankrupt wishes to pay a dividend of $1000 among four of his creditors. How much can he pay to each, if he owes A $400, B $750, C $575, and D $825?

134. WHEN THE STOCKS ARE EMPLOYED FOR UNEQUAL TIMES.

1. A and B form a partnership for 8 months. A furnishes $500 at the first. B at first furnishes but $100, but in 2 months he furnishes $600 more. What part of the gain be

longs to each?

It is, therefore, as if A furnished $4000 for 1 month, and B $4400 for 1 month. As A furnished 4000=1 of the stock, he should have of the gain; and as B furnished he should have of the gain.

88 of the stock,

Analyze the following in the same manner. Proportion.

Solve them also by

RULE. Multiply each man's stock by its time; then, as the sum of the products is to each man's product, so is the whole gain or loss to each man's share of it.

2. A and B hire a pasture for $50. 8 weeks, and B 5 cows for 7 weeks. should each pay ? How many dollars?

A pastures 3 cows for What part of the rent

3. Three persons in company contract to build a bridge. A employs 15 men for 16 weeks, B 20 men for 21 weeks, and C 30 men for 24 weeks. They gain $1500. How much of the gain should each have?

4. April 1, 1848, A commenced trade, with a capital of $1000. July 1, he admits B as a partner, who furnishes $1500. C is admitted Aug. 1; with a capital of $800. Their gains for the year ending April 1, 1849, amount to $1500. What part of the gain belongs to each ?

5. Jan. 1, 1849, A, B, and C form a partnership for one year, each contributing $2000. April 1st, A withdraws $500. May 1st, B withdraws $600, and C adds $800 more. Aug. 1st, C with draws $1000, and A furnishes $900 more. If they gain $2500, how much of it shall each have?

6. A, B, and C contract to grade 5 miles of railroad. A employs 25 men for 3 months, B 35 men for 24 months, and C 40 men for 34 months, They lose by the job $875. How much should each contribute to make good the deficiency?