he who borrows it ought to return $104. By considering the $800, as a sum so returned for what is advanced by the broker, we shall have this proportion, 104: 100 :: 800: x, whence we get $769,23† for the value of x, that is, for the sum the broker ought to give.* Questions for practice. What is the value of a cwt. of sugar at 54d. per lb. ? Ans. 2l. 11s. 4d. What is the value of a chaldron of coals at 111d. per bushel? Ans. 1l. 14s. 6d. 3 What is the value of a pipe of wine at 10 d. per pint? Ans. 441. 2s. At 3l. 9s. per. cwt. what is the value of a pack of wool, 4 weighing 2cwt. 2qrs. 13lb. کی What is the value of 1cwt. of coffee at 54d. per ounce? Ans. 617. 12s. Bought 3 casks of raisins, each weighing 2cwt. 2qrs. 25lb. what will they come to at 2l. 1s. 8d. per cwt.? Ans. 171. 4 d. 73· What is the value of 2qrs. 1nl. of velvet at 19s. 84d. per English ell? Ans. 8s. 101d. 1. Bought 12 pockets of hops, each weighing 1cwt. 2qrs. 17lb. what do they come to at 4l. 1s. 4d. per. cwt.? 96 Ans. 80l. 12s. 1d. 6. What is the tax upon 745l. 14s. 8d. at 3s. 6d. in the pound? † A sum, thus advanced, is called the present worth of the sum due at the expiration of the proposed time. * The operation by which we find what ought to be given for a sum of money, when the time of payment is anticipated, belongs to what is called Discount. There are several ways of calculating discount, but the above is the most exact, as it has regard merely to simple interest. 10 12 If of a yard of velvet cost 7s. 3d. how many yards can I buy for 13l. 15s. 6d. ? Ans. 28 yards. If an ingot of gold, weighing 91b. 9oz. 12dwt. be worth 4117. // 12s. what is that per grain? Ans. 13d. How many quarters, of corn can I buy for 140 dollars at 4s. per bushel? Ans. 26qrs. 2bu. Bought 4 bales of cloth, each containing 6 pieces, and each piece 27 yards, at 167. 4s. per piece, what is the value of the whole, and the rate per yard? 13 14 Ans. 3881. 16s. at 12s. per yard. If an ounce of silver be worth 5s. 6d. what is the price of a tankard, that weighs 1lb. 10oz. 10dwt. 4gr. 6 Ans. 61. 3s. 94d.. What is the half year's rent of 547 acres of land at 15s. 6d. per acre? Ans. 2117. 19s. 3d. 60 At $1,75 per week, how many months' board can I have for 1100l.? Ans. 47. 2w.126. Bought 1000 Flemish ells of cloth for 907. how must I sell it per ell in Boston to gain 10l. by the whole? Ans. 3s. 4d. If a gentleman's income is 1750 dollars a year, and he spends 119s. 7d. per day, how much will he have saved at the year's end? Ans. 1677. 12s. 1d. What is the value of 172 pigs of lead, each weighing 3cwt. 2qrs. 174lb. at 8l. 17s. 6d. per fother of 193cwi? Ans. 2861. 4s. 4 d. The rents of a whole parish amount to 1750l. and a tax is 2 granted of 321. 16s. 6d. what is that in the pound? 2880 Ans. 41⁄2d. 420000. If keeping of one horse be 111⁄2d. per day, what will be that of 11 horses for a year? Ans. 1921. 7s. 8d. 20993 A person breaking owes in all 14907. 5s. 10d. and has in money, goods, and recoverable debts, 784l. 17s. 4d. if these things be delivered to his creditors, what will they get on the Ans. 10s. 6d. 35767 pound? What must 40s. pay towards a tax, when 6527. 13s. 4d. is assessed at 831. 12s. 4d.? Ans. 5s. 1d. 15864. Bought 3 tuns of oil for 1517. 14s. 85 gallons of which being 2 damaged, I desire to know how I may sell the remainder per gallon, so as neither to gain nor lose by the bargain? What quantity of water must I add to a pipe of mountain wine, valued at 331. to reduce the first cost to 4s. If 15 ells of stuff, yard wide, cost 37s. of the same stuff cost, being a yard wide? 6d. per gallon? Ans. 6l. 13. 4d. Shipped for Barbadoes 500 pairs of stockings at 3s. 6d. per pair, and 1650 yards of baize at 1s. 3d. per yard, and have received in return 348 gallons of rum at 6s. 8d. per gallon, and 750lb. of indigo at 1s. 4d. per lb. what remains due upon my adventure? Ans. 247. 12s. 6d. 28 If 100 workmen can finish a piece of work in 12 days, how many are sufficient to do the same in 3 days? How many yards of matting, 2ft. 6in. broad, Ans. 400 men. will cover a floor, Ans. 72 yards. How many yards of cloth, 3qrs. wide, are equal in measure to 3030 yards 5qrs. wide? Ans. 50 yards. 2 that is 27ft. long, and 20ft. broad. A borrowed of his friend B 250l. for 7 months, promising to do him the like kindness; sometime after B had occasion for 31 3001. how long may he keep it to receive full amends for the Ans. 5 months and 25 days. 3% favor? If, when the price of a bushel of wheat is 6s. 3d. the penny loaf weigh 9oz. what ought it to weigh when wheat is at 8s. 2d. per bushel? Ans. 6oz. 13dr. If 4 cwt. can be carried 36 miles for 35 shillings, how many 33 pounds can be carried 20 miles for the same money? Ans. 907lb. 20. How many yards of canvass, that is an ell wide, will line 20 3 yards of say, that is 3qrs wide? If 30 men can perform a piece of work in 11 days, how many men will accomplish another piece of work, 4 times as large, in a fifth part of the time? Ans. 600. A wall that is to be built to the height of 27 feet, was raised 9 feet by 12 men in 6 days; how many men must be employed to finish the wall in 4 days at the same rate of working? Ans. 36. 42. 7 If oz. cost. what will 1oz. cost? 35 If 1% of a ship cost 2731. 2s. 6d. what is 5 Ans. 11. 5s. 8d. of her worth? Ans. 2271. 12s. 1d. Ans. 10 d. At 17. per cwt. what does 33lb. come to? 40 If of a gallon cost A person having 1. what will of a tun cost. Ans. 1407. of a coal mine, sells of his share for Ans. 3801. 1717. what is the whole mine worth? If, when the days are 13 hours long, a traveller perform his journey in 35 days; in how many same journey, when the days are 11 days will he perform the hours long? A regiment of soldiers, consisting of 976 men, are to be new clothed, each coat to contain 2 yards of cloth, that is 1ğyd. wide, and to be lined with shalloon, of shalloon will line them? yd. wide; how many yards Ans. 4531yds. 1qr. 2 nl. Compound Proportion. 121. PROPORTION is also applied to questions, in which the relation of the quantity required, to the given quantity of the same kind, depends upon several circumstances, combined together; it is then called Compound Proportion, or Double Rule of Three. See some examples. It is required to find how many leagues a person would go in 17 days, travelling 10 hours in a day, when he is known to have travelled 112 leagues, in 29 days, employing only 7 hours a day. This question may be resolved in two ways, we will first give the one that leads to Compound Proportion. In each case, the number of leagues passed over depends upon two circumstances, namely, the number of days the man travels, and the number of hours he travels in each day. We will not at first consider this latter circumstance, but suppose the number of hours be the same in each case; the question then will be; a person in 29 days travels 112 leagues, how many will he travel in 17 days? This will furnish the following proportion; 29: 17 :: 112: x. The fourth term will be equal to 112 multiplied by 17 and divided by 29, or 1994 leagues. 29 Now, to take into consideration the number of hours, we must say, if a person travelling 7 hours a day, for a certain number of. days, has travelled 1994 leagues, how far will he go in the same time, if he travel 10 hours a day? This will lead to the following proportion, 29 which gives for the fourth term, or answer, 93,793 leagues nearly. The question may also be resolved by observing, that 29 days' travelling at 7 hours a day, is equal to 203 hours' travelling; and that 17 days, at 10 hours a day, amounts to 170 hours; the problem then is reduced to this proportion, 203: 170 :: 112: x, by which we find the distance he ought to travel in 170 hours, according to what he performed in 203 hours. We see by the first mode of resolving the question, that 112 leagues has to the fourth term or answer, the same proportion, that 29 days has to 17, and that 7 hours has to 10; stating this in the form of a proportion, we have by which it appears, that 112 is to be multiplied by both 17 and 10, and to be divided by both 29 and 7; that is, 112 is to be multiplied by the product of 17 by 10, and divided by the product of 29 by 7, which is the same as the second method of resolving the question. 122. Again, if 9 labourers, working 8 hours a day, have spent 24 days in digging a ditch 65 yards long, 13 wide, and 5 deep, how many days will it take 71 labourers of equal ability, working 11 hours a day, to dig a ditch 327 yards long, 18 broad, and 7 deep? Here is a question very complicated in appearance, but which may be resolved by proportion. If all the condition of these two cases were alike, except the |