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DOUBLE RULE OF TIIREE, THE Double Tule of Three teaches to resolvc at once such questions as require two or more statings in simple proportion, whether direct or inverse.

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

RULE. In stating the question, place the terms of the supposition so that the principal cause of loss, gain or action pos. sess the first place; thirt 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 under the third term, the proporüon is direct; then inultiply 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 ter, the proportion is inverse; then multiply the tbiru and fourth terms together for a divisor, and the other three for a dividend, and the quotient will be the answer.

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EXAMPLES.

1. If 7 men can build 56 rods of wall in 3 days; how many rods can 20 men build in 14 days ?

3 : : 36 Terms of supposition. 20 : 14

Terms of demand. 36

84 42

50A

20

7X3=21)10080(480xods Ans. 2. If 1001. principal will gain Cl. interest in 12 months, what will 4002. gain in 7 months ? Principal 100l. : 12mo. : : 61. Int. 400 7

Ans. 1-41

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£.

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3. If 1001. will gain 61. a year ; in what time will 4001. gain 141. £

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100 : 1.2: :
400 :
:: 14

Ans. a montis. 4. If 4001. gain 141. in 7 months; what is the rate per cent. per annum ?

Int. 400 : 7 : : 14 100 : 12

Ans. £ 6. 5. What Principal at 6l. per cent. per anırum, will gain 141. in 7 months ?

Int. 100 : 12 : : 6 7:: 14

Ans. £400. 6. An usurer put out -861. to receire interest for the saine ; and when it had continued 8 months, he received principal and interest, 881. 178. 4d. ; I demand at what rate per cent. per ann. he received interest ? Ans. 5 per ct.

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

persons 12 months ?

Ans. 24 bushels. $. 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 fisth part of the time?

30 : 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 qrs. 25 Ib. 64 miles at the same rate ?

Ans. $14, 08cts. 6m. + 10. If 8 men can build a wall 20 feet long, 6 •fect 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 : : 20x6X4

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24 :

200X8X6 80 days, Ans.

CONJOINED PROPORTION, Is when the coins, weights or measures of several coun: tries are compared in the same question ; or it is joining many proportions together, and by the relation which

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several antecedents have to their conseguents, the proportion between the first antecedent and the last couscquent 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 Satings in the Single Rule of Threc, as the nature of thic question may require.

CASE I. When it is required to find low many of the first sort of coin, weight or measure, mentioned in the questival, 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 col umn; then multiply the left band column continually for a dividend, and the right hand for a divisor, and the quolient will be the answer.

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EXAMPLES.

15.

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1. If 100lb. English make 95l1). Flemish, and 19lb. Flemish 2016. at Bologna ; how many pounds English are equal to 501). at Bologna ?

lb.
100 Eng.=95 Flemish.
19 Fle. =25 Bologna.

50 Bologna. 'I'hen 95.25=25.5 the divisor. 95000 lividend, and 2875)95000(40 ans.

2. If job. at New York, make 48lb. at Antwerp, and solb. at Antwerp, make 361b. at Leghorn; how many ih. at Ne w-York are equal to 14411. at Leghorn ?

Ans. 100lb. S. If 70 'lıraces at Venice be equal to 75 braces at Leghorn, and, braces at Leghorn be equal to 4 Ainerican vards; Liow many braces ät Venicc are equal to 64 Amc. stan yards?

CASE II. Then it is required to find how many of the last sort of coin, weight or measure, mentioned in thic question, are equal to a given quantity of the fist.

jins. 104

RULE: Place the numbers alternately, beginning at the lost hand, and let thc last number stand on the right land ; then multiply the first row for a divisorand the second for a dividend.

EXAMPLES. 1. If 24b. at New-London make 20lb, at Amsterdam, anıt 50lb. at Amsterdam 60lb. at Paris; how many at Paris are equal to 40 at New-London:

Left. Night.
24 20 20' X 60 X 40 48000
50 60

--- 40 Ans.: 40 24 x 50

1200 2. If 50lb. at New-York make 45 at Amsterdam, and 80lb. at Amsterılan make 103 at Dantz.ic; how many 15: at Dantzic are equal to 240 at N. York ?

3. 11 20 braces at Leglion be equal to 11 vares at Lisbon, and 40 rares at Lisbon to 80 braces at Lucca ; How many braces at Lucca are equal to 100 braces at Leghorn

Ans. 110

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Ans. 27810

EXCHANGE, By this rule merchants know what sun of noney ought to be received in one country, for any sum of different specie paid in another, according to the given course of exchange.

To reduce the monies of foreign nations to that of the United States, you may consult the Tollowing

TABLE: Showing the value of the monics of itccount, of foreign

nations, estimated in Federal Money.* Scts. Pound Sterling of Great-Britain,

4 4 Pound Sterling of Ireland,

4 10 Livre of France,

0 181 Guilder or Florin of the U. Netherlauels, 0 39 Mark Banco of Hamburgl,

0 331 Ris Dollar of Denmark,

1 0

*Laws U. S. 1.

Rial Plate of Spain,
Milrea of Portugal,
Tale of China,
Pagoda of India,
Rupee of Bengal,

I, OF GREAT BRITAIN.

O 10 1 24 1 48 1 94

0 55

EXAMPLES.

1. In 45l. 10s. sterling, how many dollars and cents ?

A pound sterling being=444 cents, Therefore--As 1l. : 444cts. : : 45,51, : 20202cts. Ans.

2. In 500° dollars low many pounds sterling? As 444cts, : 11. : : 50000cts. : 1121. 12$. 3d.-t Ans.

II. OF IRELAND.

EXAMPLES.

£. cts.

EXAMPLES.

1. In 901. 103. 60. Irish money, how many cents ?

11. Irish=410cts.

4. cts. $ cts. Therefcre-As 1 : 410 : : 90,525 : 371151=371, 15+

2. In 168 dols. 10 cts. how many pounds Irish ?
As 410cts. : il. : : 16810cts. : £41 Trish. Ans.

III. OF FRANCE,
Accounts are kept in livres, sols and deniers.

12 deniers, or pence, make 1 sol, or shilling,

20 sols, or shillings, 1 livre, or pound. 1. In 250 livres, 8 sols, how many dollars and cents :

1 livre of France=184 cts. or 185 mills.”
£
*£

$. cts. mn. As 1 : 185 : : 250,4 : 46324346, 32 4 Ans. 2. Reduce 87 dols. 45 cts. 7 m. into livres of France.

mills. liv. mills. liv. so. den. As 185 : 1 :: 87457 : 472 14 Sant Ans.

IV. OF THE U. NETILERLANDS. Accounts are kept here in guilders, stivers, groats and phennings.

8 phennings make 1 groat.
2 groats

1 stiver.
20 stivers

1 guilder, or florin. A gui der is?9 cents, or 390 mills.

in.

M.

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