FELLOWSHIP.

6. What will 51 bbls. of cider cost, at 7 s. 6 d. per bbl. ?.

Ans. 19£ 2s. 6d. = cost, at 7 s. 6 d. per bbl

II. Hence, when the price is not an aliquot part of 1£, we nay first find what is the greatest even part, and then take parts of this part, and so on, for several times.

7. What will 20 yds. of cloth cost, at 12s. 6d. per yard? (12,10) 8. What will 40 yards of cloth cost, at 15 s. per yard? (30) 9. What will 36 bushels of corn cost, at 7 s. 6 d. per bushel? (13,10)

10. What cost 12 bbls. of ale, at 17 s. 6 d. per bbl.? (10,10) A. 66£ 10 s

11. What will 5 cwt. 3 qrs. 21 lbs. of sugar cost, at $9,60 per

ewt.?

=cost of 1 qr.

of 14 lbs.; then,

1,20

cost of 14 lbs.

,60

cost of 7 lbs.

12. At $2,50 per yard, what will 5 yds. 2 qrs. of broadcloth cost? (1375) What will 4 yds. 1 qr. cost? (10625) Will 6 yds.

3 qrs.? (16875) Ans. $41,25.

13. 5 cwt. 3 qrs. 16 lbs., at $4,20 per cwt.? (2475) 14. 3 cwt. 1 qr. 7 lbs., at $3,60 per cwt.? (11925)

15. 4 yds 2 qrs., at $2,10 per yd.?

(945)

16 4 gals. 2 qts., at $3,40 per gal.? (1530) A. $61,425.

FELLOWSHIP.

¶ LXXVII. 1. Two boys, William and Thomas, trading with marbles, in company, gained 80 cents; William owned of the marbles, and Thoma; what was each one's part of the gain

2. James and Rufus, owning a sled, in company, sold it for $3 more than it cost, that is, $3 gain; Rufus owned of it, and James what was each one's share of the gain?

Q. What is the RULE of FELLOWSHIP? A. When men are trading in company, it ascertains the gain or loss to be shared by

each.

Q. What is called STOCK, or CAPITAL? A. The money advanced or put in trade.

Q. What is called DIVIDEND? A. The gain or loss to be shared by each.

1. Three men, A, B, and C, traded in company; A put in $200, B $400, and C $600; they gained $300: what was each man's share of the gain?

In this example, it is evident, that B ought to have twice as much of the gain as A, for his stock is twice as much, and C 3 times as much as Aj that is, each man's gain or loss ought to have the same relation to the whole gain or loss, as the money he put in has to the money they all put in. The same principle will apply in all cases in which a number is to be divided into parts, which shall have a given relation, or ratio, to each other, as the dividing a bankrupt's estate among his creditors, apportioning taxes, &c. Hence, from the foregoing example, we derive the following propor

tions:

A's stock,

B's stock,

C's stock,

Whole stock, $1200) 1200 600 300

:

1200

By ratios. These are 20%, 1200, 12 = &, £, £; then, 330 x, that is, of $300 = $50, A's; † of 300 $100, B's, and

of 300 = =

$150, C's gain.

Or, by analysis. If $1200 stock gain $300, then $1 stock will gain 1200 of $300,= √1⁄2%% = $1. Now, if $1 gain $†, then ‡ of $200, A's stock, = $50, A's gain; ‡ of $400, B's stock, $100, B's gain; and of $600, C's stock,=$150, C's gain.

This last method will generally be found the shortest, and best adapted to business; especially when there are several statements, in which all the first terms are alike, and all the third terms are alike.

PROOF. It is plain, that, if the work be right, the amount of the shares of the gain or loss must be equal to the whole gain or loss; thus, in the last example, A's is $50+ B's $100+ C's $150 $300, the whole gain.

=

What, then, is the RULE? As the whole stock to each man's stock the whole gain to each man's gain.

2. Three merchants, A, B, and C, gained, by trading in com.

pany, $200; A's stock was $150, B's $250, and C's $400 · what was the gain on $1, and what was cach man's share of the gain. A. The gain on $1 is $1; then, of $150 = $37,50 A's; of $250 $02,50, B's; and of $400 = $100, C's.

3. A, B, and C, freight a ship with 270 tons; A shipped on board 96 tons, B 72, and C 102; in a storm, the seamen were obliged to throw 90 tons overboard what was the loss on 1 ton? and how many tons did each lose? A. The loss on 1 ton is of a ton; A's, 32; B's, 24; C's, 34.

4. A and B trade in company with a joint capital of $600; A put in $350,50, and B $249,50, and, by trading, they gained $120: what is the gain on $1, and what is each person's share of the gain? Ans. $; A's, $70,10; B's, $49,90.

5. A ship valued at $25200, was lost at sea, of which be longed to A, to B, and the remainder to C; what is the loss on $1, and how much will each man sustain, supposing $18000 of her to be ensured? Ans. ; A's, $2400; B's, $3600, and C's, $1200.

Perform the following examples, in the same manner, by finding how much it is for $1, or unity.

6. A detachment, consisting of 5 companies, was sent into a garrison, in which the duty required 228 men a day; the first company consisted of 162 men; the second, 153; the third, 144; the fourth, 117; and the fifth, 108; how many men must cach company furnish, in proportion to the whole number of men? A. The proportion for 1 man is; then, of 162: 54, first company; the second, 51; the third, 48; the fourth, 39; and the fifth, 36 men.

7. Two men, A and B, traded in company, with a joint capi tal of $1000; they gained $400, of which A took $300, and B the remainder; what was each person's stock? Ans. $1 gain requires 2 stock; A's, $750; B's, $250.

8. Divide $1000 between 4 persons, so that their shares may De to each other as 1, 2, 3, 4. 4. $100, $200, $300, $400.

9. A bankrupt is indebted to A $350, to B $1000, to C $1200, to D $420, to E $85, to F $40, and to G $20; his whole estate is worth no more than $1557,50: what will be each creditor's part of the property?

In adjusting claims of this nature, it is the general practica to find how much the debtor pays on $1, which is, in this case, $1. Ans. A, $175; B, $500; C, $C00; D, $210; E, $42,50; F, $20; G, $10.

10 A wealthy merchant, at his death, left an estate of $30000, to be divided among his 5 children, in such a manner that their shares shall be to each other as their ages, which vre 7, 10, 12, 15, 16 years; what was the share of each

Ans. $3500, $5000, $6000, $7500 $8000

11. A and B invest equal sums in trade, and clear $220, of which A is to have 8 shares, because he spent all his time in managing the concerns, and B, only 3 shares: what is each man's gain? and how much is A allowed for his trouble? Ans $160; A's share, $100 for his trouble; $60, B's share.

12. If a town raise a tax of $1920, and all the property in town be valued at $64000, what will that be on $1? and what will be A's tax, whose property is valued at $1200? Ans. $,03 on a dollar; A's tax, $36.

In assessing taxes, we must first make an inventory of all the property, both real and personal, of the whole town, and also of each individual who is to be taxed; and, as the whole number of polls are rated at so much each, the tax on all the polls must first be taken out from the whole tax, and the remainder is to be assessed on the property. Then, to find how much any individual must be taxed for his property, we need only find how much the remainder of the whole tax is on $1, and multiply his inventory by it.

Note. In some states taxes are assessed only on the real and personal estate of the inhabitants, no po!l taxes being allowed.

13 A certain town is taxed $2140; the whole property of the town is valued at $500000; there are 200 polls, which are taxed $,70 each; A's property is valued at $1400, and he pays for 2 polls.

polls

C's, at 1200, pays for 2

D's, 1265,

E's, 2125,

F's, 3621,

$ cls.

polls.

K's,... 265,30,

H's, at 825,50, pays for 3
I's, .800,40,
J's, 375,25,........

2

1

2

What will be the tax on $1? and what will be A's tax?

=

200 polls $70 $140, amount of the poll taxes, and $2140 $140 $2000, which is to be assessed on the property. $500000 $2000 $1,04, tax on $1. Then, to find A's tax, his inventory being $1400, we proceed thus :-

$1400 $,04 $56

polls at $,70 = $ 1,40

$57,40 A's whole tax, Ans.

What will be C's tax? (4940) What D's? (5130) What E's? (8710) What F's? (14624) What H's? (3512) What I's? 7334160) What J's? (1571) What K's? (12012)

Ans. $430,298

COMPOUND FELLOWSHIP.

¶ LXXVIII. 1. Two men hired a pasture for $9; A put in 2 oxen for 6 months, and B 3 oxen for 5 months; what ought each to pay for the pasture'

2 oxen for 6 months is the same as (2 x 6 =) 12 oxen for 1 month; and 3 oxen for 5 months is the same as (3 × 5 =) 15 sxen for 1 month.'

The shares of A and B are the same as if A had put in 12 oxen, and B 15, for 1 month each; hence the relation of 12 to 15 is the same as in Simple Fellowship, thus,

2×6=12
3 X 5 - 15

27:12:9: $4, A's. 2727:15::9: $5, B's.

Q. How, then, does Compound differ from Simple Fellowship? pound regards time, Simple does not.

Q. From the preceding example, what appears to be the

RULE?

A. Com

I. Multiply each man's stock by the time it is continued in trade.

II. Then-As the sum of the products: each man's product the whole gain or loss: each man's gain or loss.

More Exercises for the Slate.

2. Three merchants, A, B, and C, enter into partnership A puts in $60 for 4 mo., B $50 for 10 mo., and C $80 for 12 mo.; but by misfortune they lose $50: how much loss inust each man sustain ?

A's, $7,058+

Ans.

B's, $14,705-4

C's, $28,235-+

A

puts in 80 sheep sheep for 5 mo., A's, $19,20,

3. Three butchers hire a pasture for $48: for 4 mo., B 60 sheep for 2 mo., and C 72 what share of the rent must each man pay?

Ans.

B's, $7,20,
C's, $21,60.

4. Two merchants entered into partnership for 16 mo.: A at first put in stock to the amount of $600, and, at the end of 9 months, put in $100 more; B put in at first $750, and, at the expiration of 6 months, took out $250; with this stock they gained $386; what was each man's part? Ans. { A's, $200,797, B's, $185,202.

5. On the first of January, A began trade with $760, and, on the first of February following, he took in B with $540; on the first of June following, he took in C with $800; at the end of the year they found they had gained $872; what was cach man's share of the gain?

Ans. A's share, $384,929; B's, $250,71; C's, $236,36