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3. If 1001. will gain 6l. a year; in what time wiļl 400%. gain 141.
£. 100 :
:14 Ans. 7 inonths. 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 61. per cent. per annum, wil gain 141. in 7 months ? £.
Int. 100 12 : 6
7 14 Ans. £400. 6. A usurer put out 86!. to receive interest for the same ; and when it had continued 3 months, he received principal and interest, 881. 175. 4d. ; I demand at what rate per cent. per an. 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. 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 y cwt. 2qrs. 25 lb. 64 miles at the 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 : : 20 X6X4
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, tne 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 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 land 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.
1. If 100 lb. English make 95 lb. Fleinish, and 19 lb. Flemish 25 lb. at Bologna ; how many pounds English are equal to 50 lb. at Bologna ?
16. 100 Eng.=95 Flemish. 19 Fle. =25 Bologna ? 50 Bologna. Then 95 x 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. 10016. 3. If 70 braces at Venice be equal to75 braces at Leg. horn, 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.
RULE. Place the numbers alternately, beginning at the left hand, and let the last number stand on the right hand ; then mul. tiply the first row for a divisor, and the second fer a dividend.
1. If 24 lb. at New-London make 20 lb. at Amsterdam, and 50 lb. at Amsterdam 60 lb. at Paris ; how many at Paris are equal to 40 at New-London? Loft. Right.
24 = 20 20 x 60 x 40 =48000
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? Ans. 27816
3. If 20 braces at Leghorn be equal to 11 vares at Lis. bon, and 40 vares at Lisbon to 80 braces at Lucca; how many braces at Lucca are equal to 100 braces at Leghorn ?
Y this rule merchants know what sum of money ought to be received in one couatry, for any sum of different specie paid in another, according to the given course of ex. change.
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
nations, estimated in Federal money.* $ cts. Pound Sterling of Great-Britain,
4 44 Pound Sterling of Ireland,
4 10 Livre of France,
0 184 Guilder or Florin of the U. Netherlands, 0 39 Mark Banco of Hamburgh,
0 333 Rix Dollar of Denmark,
* Laws U. S. A.
Rial Plate of Spain,
I. OF GREAT BRITAIN.
1. In 451. 108. sterling, how many dollars and cents ?
A pound sterling being=444 cente, Therefore-As ll. : 444cts. : : 45,5l. : 20202cts. Ans.
2. In 500 dollars how many pounds sterling ? As 444cts. : il. : : 50000cts. : 1121. 128. 3d.t. Ans.
II. OF IRELAND.
EXAMPLES. 1. In 901. 10s. 6d. Irish
cts. $ cts. Therefore_As 1 : 410 :: 90,525 : 371153371, 15}
2. In 168 dols. 10 cts. how pounds Irish?
III. OF FRANCE.
EXAMPLES. 1. In 250 livres, 8 sols, how many dollars and cents
i livre of France=18 cts. or 185 mills.
$ cts. mo As 1 : 185 :: 250,4 : 46324546, 32 4 Ans. 2. Reduce 87 dols. 45 cts. 7 m. into livres of France.
mills. liv. mills. liv. so. den.
IV. OF THE U. NETHERLANDS. Accounts are kept here in guilders, stivers, groats and phennings.
8 phennings make 1 groat.
1 guilder, or florin. A guilder is 39 cents, or 390 millo.
Reduce 124 guilders, 14 stivers into federal money.
Guil. cts. Guil. $ d. As 1 : 39: 124,7 : 48, 6 3 3 Ans. mills.
mills. As 390 : 1 :: 124,7 Proof. V. OF HAMBURGH, IN GERMANY. Accounts are kept in Hamburgh in marks, sous and deniers-lubs, and by some in rix-dollars.
12 deniers-lubs make I sous-lubs.
1 mark-lubs. 3 mark-lubs, 1 rix-dollar. NOTE:-A mark is=33} cts.or just Ž of a dollar
RULE. Divide the marks by 3, the quotient will be dollars.
Reduce 641 marks, 8 sous, to federal money.
$213,833 Ans. But to reduce federal money into marks, multiply the given sum by 3, &c.
Reduce 121 dollars, 90 cts. into marks banco. 121,90
365,70=365 marks, 11 sous, 2,4 den. Ans.
YI. OF SPAIN. Accounts are kept in Spain in piastres, rials, and mar. vadies.
34 marvadies of plate make 1 rial of plate.
1 piastre or piece of 8. To reduce rials of plate to Federal Money. Since a rial of plate is = 10 cents or 1 dinie, you need only call the rials so many dimes, and it is done.
435 rials 485 dimess48 dols. 50 cts. c.