2. If £100 in one year gain £6 interest, what will be the interest of £750 for 7 years?

1 year

: £6 ::

(7 years }

£750

: £315 Ans. £100 3. A farmer sells 204 dollars' worth of grain in 5 years, when it sold at 60 cents per bushel; what is it per bushel when he sells 1000 dollars' worth in 18 years, if he sell the same quantity yearly? Ans. 81cts. 6mills. +

4. If 7 men can reap 84 acres of wheat in 24 days, how many men can reap 100 acres in 10 days? Ans. 20 men.

5. If 6 men build a wall 20 feet long, 6 feet high and 4 feet thick, in 16 days; in what time will 24 men build one 200 feet long, 8 feet high and 6 feet thick?

24 men
20 feet long
6 feet high
4 feet thick

Ans. 80 days.

6 men
200 feet long

: 16 days ::

: 80 days.

8 feet high

6 feet thick

6. An usurer put out 75 dollars at interest, and at the end of 8 months he received for principal and interest, 79 dollars; I demand at what rate per cent. he received interest. Ans. 8 per cent.

7. If the carriage of 18ewt. 1qr. for 72 miles be £2 10s. 6d. what will be the carriage of 7cwt. 3qrs. for 112 miles? Ans. £25s. 11d. 1 757qr.

8. If a family of 9 persons spend 450 dollars in 5 months, how much would be sufficient to maintain them 8 months, if 5 more were added to the family?

6

Ans. 1120 dollars.

9.. What is the interest of 654 dollars for 164 days, at per cent. per annum? Ans. 17 dolls. 63cts. 1m.+ 10. If 248 men in 5 days of 11 hours each, dig a trench 230 yards long, 3 yards wide and 2 deep; in how many days of 9 hours long, will 24 men dig a trench 420 yards long, 5 wide and 3 deep? Ans. 2885 days.

11. If 30 men perform a piece of work in 20 days, how many men will effect another piece of work, 4 times as large, in a fifth part of the time? Ans. 600 men.

12. What principal will gain $315 in 7 years, at 6 per cent. per annum? Ans. $750. 13. If 3000. of beef will serve 340 seamen 15 days, how many pounds will serve 120 seamen 25 days? Ans. 1764. 1lfoz

CONJOINED PROPORTION.

CONJOINED PROPORTION is when the coins, weights, or measures of several countries, are compared in the same question; or it is the joining together of several ratios, and inferring the ratio of the first antecedent and last consequent, from the ratios of the several antecedents and their respective consequents.

CASE I.

When it is required to find how many of the last kind of coin, weight, or measure, mentioned in the question, are equal to a given number of the first.

RULE 1.-Multiply continually together the antecedents for the first term, and the consequents for the second, and make the given number the third.

2. Then find the fourth term or proportional, which will be the answer required.

EXAMPLES.

1. If 10. at Boston make 9ft. at Amsterdam; 90. at Amsterdam 112. at Thoulouse, how many . at Thoulouse are equal to 50†. at Boston ?

1008: 50: 56ff. Ans.

900 :

2. If 20 brasses at Leghorn be equal to 10 varas at Lisbon; 61 varas at Lisbon to 75 American yards; how many American yards are equal to 100 brasses at Leghorn ? Ans. 61 yards.

CASE II.

When it is required to find how many of the first kind of coin, weight, or measure, mentioned in the question, are equal to a given number of the last.

RULE.-Proceed as in the first case, only make the product of the consequents the first term, and that of the an

tecedents the second.

EXAMPLES.

1. If 20 ells English make 11 canes at Rome; 44 canes at Rome, 136 brasses at Venice; how many ells English make 85 brasses at Venice ?

Ant.

Con.

20 : 11

44 :

880

136

1496: 880 :: 85: 50 ells, Ans.

2. If 41 U. S. hushels make 26 hanegas at Cadiz; 39 hanegas at Cadiz, 162 alquiers at Lisbon; 27 alquiers at Lisbon, 5 sacks at Leghorn; and 20 sacks at Leghorn, 21 tuns at Copenhagen; how many U. S. bushels make 36 tuns at Copenhagen? Ans. 70 bus.

3. If 300 U. S. miles make 77 miles in Germany; 1771 miles in Germany, 1250 posts in France; and 25 posts in France, 38 miles in Holland; how many U. S. miles make 80 in Holland? Ans. 29018 U. S. miles.

BARTER.

BARTER is the exchanging of one commodity for anoth er, and directs traders so to proportion their goods, that neither party may sustain loss.

RULE.*-Find the value of that commodity the quantity of which is given; then find what quantity of the other, at the rate proposed, you may have for the same money, and it gives the answer required.

EXAMPLES.

1. How many dozen of candles, at 3s. 6d. per dozen, must be given in barter for 4cwt. 2qrs. of tallow, at 46s. per cwt.?

* This rule is only an application of the Rule of Three.

s. d.

doz.

3 6 .: 2. A buys of B 4 hogsheads of wine containing 410 gallons, at 1 dollar 17 cents per gallon; and 253. of coffee at 21 cents per ft. In part of which he pays him 21 dollars in cash, and the balance in boards at 8 dollars per thousand; how many feet of boards does the balance require? Ans. 63978 feet.

1 :: 10 7 : 59doz. 1+Ans.

3. Bought a sloop of 70 tons at 16 dollars per ton; paid in cash 500 dollars, 350 gallons of molasses at 64cts. per gallon, and the balance in oil at 74 cts. per gallon; how many gallons did it amount to?

Ans. 535 gal.

4. A barters with B 150 bushels of wheat at 5s. 9d. per bushel, for 65 bushels of corn at 2s. 10d. per bushel, and the balance in oats at 2s. 1d. per bushel; what quantity of oats must A receive? Ans. 325 bushels.

5. How much wine at 1 dollar 28 cents per gallon, must I receive in barter for 26cwt. 2qrs. 14ft. of raisins, at 9 dollars 44 cents 4 mills per cwt., 25. a qr.?

Ans. 196gals. 2qts. 1,704gills. 6. A delivers B 3 hogsheads of wine at 6s. Sd. per gallon, for 126 yards of cloth; what was the cloth per yard, in Federal Money? Ans. 1 dollar 66 cts.

7. A has a quantity of pepper, weight neat 1600. at 1s. 5d. per . which he barters with B for two sorts of goods, the one at 5d. the other at 8d. per pound, and to have in money, and of each sort of goods an equal quantity; how many t. of each must he receive, and how much in money?

Ans. 139434lb. of each, and £37 15s. 63d.

8. A and B barter; A has 145 gallons of oil, at $1,20cts. per gallon ready money, but in barter he will have $1,35cts. per gallon; B has linen at 58 cents per yard ready money; how must B sell his linen per yd., in proportion to A's barter price, and how many yards are equal to A's oil?

Ans.

B's linen is 65cts. 24m. barter price, and

he must give A 300yds. for his oil. 9. K and L barter; K has woollen cloth worth $1,33 cts. per yard, which he barters at $1,54cts. with L., for linen cloth at 50cts. per yard, which is worth 43cts. per yard;-who has the advantage in barter, and how much linen does L give K for 70 yards of woollen?

Ans. 215 yds. of linen, and L. has the advantage, his proportional barter price being only 491 cts. 10. J. Tucker and Jonathan Olmstead barter; the former gives the latter 90 gallons of wine at $1,28 per gallon; for which the latter gives the former 10 guineas at 28s. each, in money, and 500. of cotton;-what is it valued at per pound? Ans. 13 cts.

11. Giles Jackson has 100 reams of paper, at $1,331 cts. ready money, which in barter he sets down at $1,663 cts. Robert Howard, sensible of this, has pamphlets at 8 cts. apiece ready money, which he adequately charges, and insists, besides, on of the price of those he parts with, in money;-what number of the books is he to deliver in lieu of Jackson's paper? what cash will make good the difference? and how much is Howard the gainer by this affair? Ans. 1600 books to be delivered; $41,66%cts. Howard is to have in cash; and the gain to Howard is $41,66 cts.

LOSS AND GAIN.

Loss AND GAIN is a rule that discovers what is gained or lost in buying or selling goods; and instructs merchants and traders to raise or lower the price of their goods, so as to gain or lose a certain sum per cent.

Questions in this rule are performed by the Rule of Three.