6. A captain, mate, and 20 seamen, took a prize worth 3501 dols. of which the captain takes 11 shares, and the mate 5 shares; the remainder of the prize is equally divided among the sailors; how much did each man receive?

Ans. The captain received
The mate

Each sailor

$cts. 1069, 75

486, 25

97, 25

7. Divide the number of 360 into 3 parts, which shall be to each other as 2, 3 and 4. Ans. 80, 120 and 160.

8. Two merchants have gained 4501. of which A is to have three times as much as B; how much is each to have? Ans. A £337 10s. and B £112 10s.-1+3=4 ; 450 : :

3: £337 10s. A's share.

9. Three persons are to share C007. A is to have a certain sum, B as inuch again as A, and C three times as much as B. I demand each man's part?

Ans. A £66, B £1333, and C £400. 10. A and B traded together and gained 100 dols. A put in 640 dols. B put in so much that he must receive 60 dols. of the gain; I demand B's stock? Ans. $960.

11. A, B and C traded in company: A put in 140 dols. B 250 dols. and C put in 120 yds. of cloth, at cash price; they gained 230 dols. of which C took 100 dols. for his share of the gain: how did C value his cloth per yard in common stock, and what was A and B's part of the gain? Ans. C put in the cloth at $2 per yard. A gained $46, 67 cts. 6 m. and B $83, 33 cts. 3 m.+

COMPOUND FELLOWSHIP,

OR Fellowship with time, is occasioned by several shares of partners being continued in trade an unequal term of time.

RULE.-Multiply each man's stock, or share, by the time it was continued in trade then,

As the sun of the several products,

Is to the whole gain or loss:

So is each man's particular product,

To his articular share of the gain or loss.

EXAMPLES.

1. A, B and C hold a pasture in common, for which they pay 197. per annum. A put in 8 oxen for 6 weeks; B 12 oxen for 8 weeks; and C 12 oxen for 12 weeks; what must each pay of the rent?

S. d.

48: 3

3 4 A's part.

96 : 6

68 B's

144

9

Proof 19 0 0

2. Two merchants traded in company; A put in 215 dols. for 6 months, and B 390 dols. for 9 months, but by misfortune they lose 200 dols.; how must they share the loss? Ans. A's loss $53, 75 cts. B's $146, 25 cts.

3. Three persons had received 665 dols. interest: A had put in 4000 dollars for 12 months, B 3000 dollars for 15 months, and C 5000 dollars for 8 months; how much is cach man's part of the interest?

Ans. A $240, B $225, and C $200. 4. Two partners gained by trading 1107. 12s. : A's stock was 1201. 10s. for 4 months, and B's 2001. for 6 months; what is each man's part of the gain?

426

Ans. A's part £29 18s.31d.¦¦ B's £80 13s. 81d. Af

5. Two merchants enter into partnership for 18 months. A at first put into stock 500 dollars, and at the end of 8 months he put in 100 dollars more; B at first put in 800 dollars, and at 4 months' end took out 200 dols. At the expiration of the time they find they have gained 700 dollars; what is each man's share of the gain?

Ans.

$324, 07 4+ A's share,
$375, 92 5+B's do.

6. A and B companied; A put in the first of January, 1000 dollars; but B could not put in any till the first of May; what did he then put in to have an equal share with A at the year's end?

Mo.

As 12

Mo.

1000 :: 8: 1000×12=1500 Ans.

DOUBLE RULE OF THREE.

THE Double Rule of Three teaches to resolve at once such questions as require two or more statings in simple proportion, whether direct or inverse.

In this rule there are always five terms given to find a sixth; the first three terms of which are a supposition, the last two a demand.

RULE. In stating the question, place the terms of the supposition so that the principal cause of loss, gain, or action, possess the first place; that which signifies time, distance of place, &c. in the second place; and the remaining term in the third place. Place the terms of demand, under those of the same kind in the supposition. If the blank place, or term sought, fall une der the third term, the proportion is direct; then multiply the first and second terms together for a divisor, and the other three for a dividend: but if the blank fall under the first or second term, the proportion is inverse; then multiply the third and fourth terms together for a divisor, and the other three for a dividend, and the quotient will be the answer.

EXAMPLES.

1. If men can build 36 rods of wall in 3 days; how many rods can 20 men build in 14 days?

7: 3: 36 Terms of supposition.

20: 14

36

84

42

504

20

Terms of demand.

7x3=21)10080(480 rods. Ans.

2. If 1007. principal will gain 67. interest in 12 months, what will 4007. gain in 7 months?

Principal 1007. 12mo.:: 6l, interest.
400 : 7

Ans. 147,

3. If 1007. will gain 67. a year; in what time will 4007. gain 141. £. mo. £

100 : 12: : 6

400 : ::14 Ans. 7 months.

4. If 4007. gain 147. in 7 months: what is the rate per cent. per annum?

£. mo. Int.

400 : 7 :: 14
100 : 12

Ans. £6.

3. What principal at 6l. per cent. per annum, will give 14. in 7 months?

£. mo. Int.

100: 12::

6

6. An usurer put out 867, to receive interest for the same; and when it had continued 8 months, he received principal and interest, 887. 17s. 4d.; I demand at what rate per ct. per ann. he received interest? Ans. 5 per cent.

7. If 20 bushels of wheat are sufficient for a family of 8 persous 5 months, how much will be sufficient for 4 persons 12 months?

Ans. 24 bushels. 8. If 30 men perform a piece of work in 20 days; how many men will accomplish another piece of work 4 times as large in a fifth part of the time?

80: 20 :: 1
4:: 4

Ans. 600.

9. If the carriage of 5 cwt. 3 qrs. 150 miles, cost 24 dollars 58 cents; what must be paid for the carriage of 7 cwt. 2 qre. 25 lb. 64 miles, at the same rate?

Ans. $14, 08 cts. 6m.+ 10. If 8 men can build a wall 20 feet long, 6 feet high, and 4 feet thick, in 12 days; in what time will 24 men build one 200 feet long, 8 feet high, and 6 feet thick? 8: 12 :: 20×6×4

CONJOINED PROPORTION,

IS when the coins, weights or measures of several countries are compared in the same question; or it is joining many proportions together, and by the relation which

several antecedents have to their consequents, the propor tion between the first antecedent and the last consequent is discovered, as well as the proportion between the others in their several respects.

NOTE. This rule may generally be abridged by cancelling equal quantities, or terms that happen to be the same in both columns: and it may be proved by as many statings in the Single Rule of Three as the nature of the question may require.

CASE I.

When it is required to find how many of the first sort of coin, weight or measure, mentioned in the question, are equal to a given quantity of the last.

RULE.-Place the numbers alternately, beginning at the left hand, and let the last number stand on the left hand column; then multiply the left hand column continually for a dividend, and the right hand for a divisor, and the quotient will be the answer.

EXAMPLES.

1. If 100 lb. English make 95 lb. Flemish, and 19 lb. Flemish 25 lb. at Bologna; how many pounds English are equal to 50 lb. at Bologna?

7b.

lb.

100 Eng. 95 Flemish,

25 Bologna,

19 Fle.

50 Bologna.

Then 95 × 25=2375 the divisor.

95000 dividend, and 2375)95000(40 Ans.

2. If 40 lb. at New-York make 48 lb. at Antwerp, and 30 lb. at Antwerp make 36 lb. at Leghorn; how many lb. at New-York are equal to 144 lb. at Leghorn?

Ans. 100 lb 3. If 70 braces at Venice be equal to 75 braces at Leghorn, and 7 braces at Leghorn be equal to 4 American yards; how many braces at Venice are equal to 64 American yards? Ans. 104.

CASE II.

When it is required to find how many of the last sort of coin, weight or measure, mentioned in the question, are equal to a given quantity of the first.