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EXAMPLES

1. A, B and C hold a pasture in common, for which they pay 191. 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

d. 8x 6= 48

48 : 3 3 12x 8 96

96 : 6

6 8 B's 12x12=144 } As 288 : 191. :: 144 : 9 10 O C's

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4 A's pt.

Proof 19

Sum 288,

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, 75cts. B's $146, 25cts.

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

Ans. A $240, B $225 and C $200. 4. Two partners gained by trading 1101. 125. : A's stock was 1201. 10s. for 4 months, and B's 2001. for 64 months ; what is each man's part of the gain ? Ans. A's part £29 18s. 3:1d.jan. B’s £80 13s. 8 1.48285

5. Two merchanis 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 month's 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 dols. ; 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.

Mo.
As 12 1000 :: 8 : 1000x12=1500 Ans.

DOUBLE RULE OF THREE. THE

HE Double Rule of Three teaches to resolve at once such questions as require two or more statings in simpie pre portion, whether direct or inverse.

In this rule there are always five terms 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 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 under 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 divi dend, and the quotient will be the answer.

EXAMPLES,

1. If 7 men can build 36 rods of wall in 3 days ; bon many rods can 20 men build in 14 days?

3: : 36 Terms of supposition. 20 : 14

Terms of demand. 36

7 :

84

504

20

7x321)10080( 480 rods. Ans. 2. If 1001. principal will gain 61. interest in 12 months, . what will 4007. gain in 7 months ? Principal 1001. : 12no. : : 61. Int. 400 7

Ars. 141.

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mo.

mo.

3. If 100% will gain ol. a ycar ; in wiiat time will 4001. gain 141.

100 : 12 :: 6
400 :

::14

Ans. 7 months. 4. If 4001. gain 141. in 7 months : what is the rate per cent. per annum ? £.

Int.
400 :

7 :: 14
100.:
12

Anis. £6. 5. What Principal at Cl. per cent. per annum, will gain 141. in 7 months ? £.

Int. 100 : 12 :: 6

7 :: 14 Ans. £400. 6. An usurer put out 861. to receive interest for the same ; and when it had continued 8 months, he received principal and interest, 881. 17s. 4d. ; I demand at what rate per cent. per ann. he received interest ? Ans. 5 per ct.

7. If 20 bushels of wheat are suficient for a family of 8 persons 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 ?

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 lb. 64 miles at the same rate

Ans. $14, 08cts. 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 : : 20x6x4

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

several antecedents have to their consequents, the proportion 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 can celling equal quantities, or terms that happen to be the same in both columns : and it may be proved by as muy statings in the Single Rule of Three as the nature of the question may require.

CASE 1. 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 ine 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 Flenuish 25 lb. at Bologna ; how many pounds English are erjual to 50 lb. at Bologna ? Zb.

16.
100 Eng.–95 Flemish.
19 Fle. 25 Bologna ?
50 Bologna

Then 95%25=2375 the divisor. 95000 lividend, and 2375 95000(40 Ins.

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

Ans. 10016. 3. I 70 braces it Venice be equal to 75 braces at Leghorn, and 7 braces ai leghorn be equal to 4 American yards ; how many braces at Venice are equal to 64 American yards ?

Ans. 104,85.

CASE II. When it is requiri? :v find how many of the last sort of cain, weight or to Use', mentioned in the question, are equal to a given whay vi the first.

RULE. Place the numbers alternately, beginning at the left hand, and let the last number stand on the right hand, then multiply the first row for a divisor, and the second for a dividenu.

EXAMPLES.

1. If 24 lb. at New-London make 20 lb. at Amsterdam, and 50 lb. at Amsterdam 60 lb. at Paris ; low many at Paris are equal to 40 at New-London ? Left. Right. 24 20 20 X 60 X. 40 = 48000 50 60

40 Ans. 40 24 x 50 =

1200 2. If 50 lb. at New-York make 45 at Amsterdam, and 80 lb. at Amsterdam make 103 at Dantzic; how many lb. at Dantzic are equal to 240 at N. York ? ins. 27815

3. If 20 braces at Leghorn be equal to 11 vares at Lisbon, and 40 vares at Lisbon to 80 braces at Lucca ; how many braces at Lucca are equal to 100 braces at Leghorn ?

ins, 110.

EXCHANGE. By this rule merchants know what sum of money ought to be received in one country, for any sumn 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 following

TABLE: Showing the value of the monies of account, of foreign da. tions, estimated in Federal money.*

$ cts. Pound Sterling of Greai-Britain, Pound Sterling of Ireland, Livre of France,

O 185 Guilder or Florin of the U. Netherlands,

39 Mark Banco of Hamburghi,

033} Rix Dollar of Denmark,

4 44 4 10

1

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* Laros V. S. 1.

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