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4. What will 34964yards come to, at two farthings per yard?

Ans. £72 16s. 10đ. Case II.—When the price is given in pence, or in pence and farthings.

RULE.-Suppose the yards, pounds, &c. to be so many shillings; and if there be of a yard, call it 3 pence; if there be $ of a yard, call it 6 pence; and of a yard, call it 9 pence. Then take aliquot parts of a shilling or the price, at one shilling a yard for the given price,

EXAMPLES. 1. What will 3967 yards come to at 9 pence per yard ?

Ans. £14 17s. 4.1d. d. d.

2. What will 864 yds. 6=}}396 6

come to, at 4 pence per 3=1)198 3 price at 6d. per yd.

yard? Ans. £14 8s. 99 1 € price at 3d. per yd.

3. What will 34845 210)297 4 1 price at 9d. per yd.

yds. cost, at 3d. per yd.?

Ans. £43 11s. Od. 3qrs. Ans. £14 17s. 4d. 2qrs.

4. What will 3050 yards come to, at 8 pence per yard?

Ans. £101.135. 4d. CASE III.-When the price of one yard, or one pound, is shillings, or shillings and pence,

RULE.-Suppose the number of yards, or pounds, to be so many pounds in money; and if there be 4 of a yard, call it 5 shillings; if of a yard, call it 10 shillings; if of a yard, call it 15 shillings; then as it stands, at £i per gard, take aliquot parts for the given price per yard. 1. What will 8963 yards cost, at 5 shillings per yard?

Ans. £99 2s. 6d. £

2. What will 980 yards come to, at 5=*)396 10 15s. per yard?

Ans. £735. 3. What will 384 yards come to, at Ans. £99 28. 6d. 12s. per yard?

Ans. £230 85. 4. What will 980 yards come to, at £2 5 shillings per yard?

Ans. £2205. NOTE.—When the price of one yard exceeds £l; maltiply the given quantity standing at £1 per yard, by the number of pounds per yard; and then take, as in the other examples, parts for the shillings

3.

S.

and pence.

QUESTIONS ON PRACTICE: What is Practice? A. A contraction of the Rule of Three Direct. How would the questions be stated in the Rule of Three? A. As llb or ) yard, is to the price of 1 lb. or one yard, so is the given number of pounds or yards, to the price of the whole quantity. Can it be performed by multiplication? A. It can, by multiplying the price of one yard or one pound by the whole quantity; or the whole quantity multiplied by the price of one yard or one pound, will give the price of the quantity: When the price is given in farthings, what do you suppose the yards to be? A. So many pence, and then take aliquot parts. When the price of one yare or one pound is given in pence, what do you suppose the given quantity to be? A. So many shillings, and take aliquot parts. When the price of one yard or one pound is given in shillings, what do you suppose the given number of yards or pounds to be ? A. So many pounds sterling, and then take aliquot parts of the price, at £1 per yard or pound.

SINGLE FELLOWSHIP, Is only another name given to the Rule of Three Direct, when applied to the business of merchants, and others trading in company. Its principles are applied in finding each man's share of the gain or loss in trade, in proportion to his stock. In Single Fellowship, partners continue their stock in trade an equal term of time.

RULE.-As the whole'stock is to the whole gain or loss, so is each man's stock to his share of the gain or loss,

Note:—This rule may be applied in adjusting a bankrupt's estate among his creditors; for as the sum of the debts due to the creditors is to the bankrupt's estate, so is each creditor's demand to his share of the bankrupt's estate. But it would reduce it to greater simplicity, to work by Multiplication and Division ; first dividing the whole estate by the sum of the debts, and the quotient will be the sum to be received on a dollar, and this quotient multiplied by each creditor's demand, will give, separately, each creditor's share of the estate. It will in the same manner apply in making out a tax fist; for as the amount of property is to the tax to be levied, so is each man's estate to his share of the tax. A school bill may be made out in the same way; for as the sum of the days sent is to the teacher's wages, so is each person's number of days to his bill; but the better way to make oùt a tax list or school bill, is to reduce the work to Multiplication and Division.

EXAMPLES 1. Two merchants trading in company, gained $800; A's stock was $1800, B's $1400; what was each man's share of the gain?

Ans.

$350 B's share. A's stock, $1800 B's stock, $1400 3200 : 800 ::

$450 A's share. S 1800

: Ans 1400

$350 B's share.

800 PROOF. By adding the several shares of gain or loss.

[graphic]

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DEM.--It is evident, that the operation here, is as in the Rule of Three Direct, and that each man's share of the gain, is in proportion to his stock. $1800 Same example by Division and Multiplication: $1400 $ 3200)800,00 ( ,25 cents on a dollar. 640,0 1800

1400 160,00 20000

10000 160,00

25 0 $450,00 A's share. $350,00 B's share. 2. A, B, and C companied; A put in $400, B 600; C:800 dollars; they gained 540 dollars; what must each have of the gain?

Ans. A's share 120, B's 180, C's $240. 3. Divide 742 dollars between A, B, and C, so that B shall have twice as much as A, and C twice as much as B; what will be the share of each?

Ans. A's 106, B's 212, C's $124. 4. A captain, mate, and 20 seamen, took a prize worth 4674 dollars; of which the captain is to have 12 shares, and the mate 6 shares; the remainder is to be divided equally among the seamen; how much is each person's share?

Ans.

The captain's share is $1476, the mate's

$738, each seaman's share $123. QUESTIONS ON SINGLE FELLOWSHIP. What is Single Fellowship? A. the Rule of Three Direct applied to the business of partners in trade, to ascertain each man's share of the gain or loss. Why does this belong to the Rule of Three ? A. Because it is evident ihat each man's share of gain or portion of loss, must be in proportion to his stock: Can Fellowship be worked by Multiplication and Division ? A. It can, by dividing the whole gain by the whole stock; the quotient will be the gain on a dollar, and that repeater by each man's stock will give the gain of each.

DOUBLE FELLOWSHIP. In Double Fellowship, or Fellowship with time the stocks are con tinued in Trade unequal times. This rule, as well as Single Fellowship, belongs strictly to the Rule of Three Direct.

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

EXAMPLES. 1. Three persons traded in company; A put in 100 dol lurs for 2 years, B 400 dollars for 4 years, and C 200 dol.:

{

lars for 9 years; they gained 600 dollars; what must each have of the gain?

Ans. A$400X2= 800

800 : $120 A's sh. B 400X4=1600

1600 ; 240 B's sh. Aş 4000 : 600 :: C 200X8=1600

1600 : 240 C's sh. Sum, 4000.

Proof, 3600 DEM.-From the example given, it is evident that this is strictly the Rule of Three Direct, and each person's share of gain or loss, must be in proportion to his product of money and time. A's share of gainis only one half as much as B's, because his money is invested in trade only half as long; and C's is equal to B's, because he has half as much money as B, invested in trade double the time; and it is plain, that 200 dollars must gain as much in 8 years as 400 dollars in 4 years.-This can be reduced back to Multiplication and Division, by dividing the whole gain, 600 dollars, by the sum of the products; the quotient, which would be the gain on a dollar, must then be multiplied separately by each man's product for the gain of each.

2. Two partners gained by trading, 800 dollars; A's stock was 1200 dollars for 8 months, and B's $800 for 10 months; what is each partner's share of the gain?

Ans. A's share $436,36cts. 3m., B's 8363,63cts. 6m. • 3. A, B, and C, entered into partnership; A, put in 8400 for 6mo.; B, $250 for 8mo.; C, $360 for 5 mo.; on adjusting their accounts they find their loss to be $638 ; what is cach man's loss? Ans. A's loss $240, B's. $200, C's $198

QUESTIONS ON DOUBLE FELLOWSHIP. Wherein does Double Fellowship differ from Single Fellowship? A. In Double Fellowship, the stocks are continued in trade unequal times, which is not the case in Single Fellowship. Does Double Fellowship depend on the Rule of Three Direct the same as Single Fellowship? A. Just the same, and may be reduced back to division and multiplication. How is the work prepared for a statement, in the Rule of Three ? A. By multiplying each man's stock by the time it was continued in trade, and then adding the several products; then say, as the sum of the products, is to the whole gain or loss, so is each man's product, to his share of the gain or loss.

BARTER, Is exchanging one commodity for another, according to the price or value agreed apon by the parties concerned. It is merely an application of the Rule of Three Direct to the exchange of specifick articles, so that neither party shall sustain a loss. The operation is frequently easier performed by multiplication and division.

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RULE.-Kind the value of the commodity; whose quantity is given, then find what quantity of the other, at the proposed rate, can be purchased for the same money, and it will give the answer.

EXAMPLES. 1. How much corn, at 40cts. a bushel, must be given for 60 bushels of wheat, at 80cts. a bushel ? Ans. 120 bushels.

By Multiplication and Division. bu, cts. bu.

cts.

DEM.- It is plain, 1:,80 :: 60

,80

when we repeat the 60

60

price of 1 bushel of

wheat, by the num. ,40)48,00(120 Ans. ,40148,00€ 120 Ans. ber of bushels, that

40

the product is the

price of the whole quantity; 80

80

then, when we divide the 80

80 whole cost of the wheat, by Ö

the price of 1 bushel of com, 0

the quotient must be the quantity of corn; because as often as the sum of 40 cents is contained in the whole money, so often a bushel of corn can be had in exchange for the wheat.

2. What quantity of butter, at 10-cents a pound, must a lady give in barter for 8 yards of satin, at 1 dollar 25 cents per yard?

Ans. 100 pounds. When the quantities of both commodities are given, and the difference of their values is to be paid in money ; find the value of both, and the difference of their values will be the answer.

When one commodity is rated above cash price, to find the bartering price of the other, say, as the cash price of the one, is to its bartering price, so is the cash price of the other, to its bartering price.

3. A, lets B, have 50 bushels of rye, at 45 cents a bushel, for which he receives 60 bushels of oats, at 25 cents a bushel, and the balance in money, how much money must A re: ceive?

Ans. $7,50 cents. 4. A, has calico worth 18cts. a yd., ready money, but in bar. ter he will have 25 cents; B, has broadcloth worth $3,75cts. per yard, ready money; at what price ought the broadcloth to be rated at in barter ?

Ans. $5,20 cents, 8 mills. QUESTIONS ON BARTER. What is barter ? A. It is strictly the Rule of Three Direct applied to the exchange of one commodity for another, so that neither party shall sustain foss. When you have the price of one quantity or cona. modity, how do you find the quantity of the other commodity, which may be received for the money? A. Divide the money by the price

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