When one of the ingredients is limited to a certain quantity. RULE. Take the difference between each price and the mean rate, as before; then, As the difference of that simple, whose quantity is given, is to the rest of the differences severally, so is the quantity given, to the several quantities required. EXAMPLES. 9. How much wine, at 5s. at 5s. 6d. and at 6s. the gallon, must be mixed with three gallons, at 4s. per gallon, so that the mixture may be worth 5s. 4d. per gallon? Ans. 3 gallons at 5s.; 6 at 5s. 6d. and 6 at 6s. 10. A grocer would mix teas at 12s. 10s. and 6s. with 20 Ib. at 4s. per lb. ; how much of each sort must he take to make the composition worth 8s. per lb. ? 11. Ans. 20 lb. at 4s.; 10 lb. at 6s. ; 10 lb. at 10s. ; and 20 lb. at 12s. How much gold of 15, of 17, and of 22 carats fine, must be mixed with 5 oz. of 18 carats fine, so that the composition may be 20 carats fine? Ans. 5 oz. of 15 carats fine, 5 oz. of 17, and 25 of 22. ...... POSITION. POSITION is a rule, which, by false or supposed numbers, taken at pleasure, discovers the true one required. ded into two parts, SINGLE and DOUBLE. SINGLE POSITION It is divi Is, by using one supposed number, and working with it as the true one, you find the real number required by the following RULE. As the total of the errors is to the given sum, so is the supposed number to the true one required. PROOF. Add the several parts of the result together, and if it agrees with the given sum, it is right. EXAMPLES. 1. A school-master, being asked how many scholars he had, said, If I had as many, half as many, and one quarter as many more, I should have 264; how many had he? Suppose he had 72 As many as many ...... 72 .36 .... 18 and of his money, had 60 Ans. 144 dols. 2. A person, after spending dollars left; what had he at first? 3. A certain sum of money is to be divided between 4 persons, in such a manner, that the first shall have of it, the second, the third, and the fourth the remainder, which is 28 dollars; what was the sum ? Ans. 112 dols. 4. A person lent his friend a sum of money unknown, to receive interest for the same, at 6 per cent. per annum, simple interest, and at the end of 5 years he received for principal and interest 644 dollars 80 cents; what was the sum lent? Ans. 496 dols. ...... DOUBLE POSITION Is, by making use of two supposed numbers, which, if both prove false, are, with their errors, to be thus disposed: RULE. 1. Place each error against its respective position. 2. Multiply them cross wise, 3. If the errors are alike, that is, both greater or both less than the given number, divide the difference of the products by the difference of the errors, and the quotient is the answer: But if the errors be unlike, divide the sum of the products by the sum of the errors, and the quotient will be the answer. EXAMPLES. 1. B asked C how much his horse cost; C answered, that if he cost him three times as much as he did, and 15 dollars more, he would stand him in 300 dollars; what was the price of the horse ? 285 too lit. by 15 dls. 303 too much by 3 dls. Sum of the errors 18) 1710 (95 answer 162 90 95 3 285 15 - 300 proof. 2. Two persons, A and B, have both the same income; À saves one-fifth of his yearly but B, by spending 150 dollars per annum, more than A, at the end of 8 years finds himself 400 dollars in debt; what is their income, and what does each spend per annum ? Ans. Their income is 500 dollars per annum ; also A spends 400, and B 550 dollars per annum. 3. There is a fish whose head is 9 inches long, and his tail is as long as his head and half his body, and his body is as long as the head and tail; what is the whole length of the fish? Ans. 6 feet. 4. Divide 15 into two such parts, so that when the greater is multiplied by 4, and the less by 16, the products will be equal. Ans. 12 and 3. 5. A man had two silver cups of unequal weight, having one cover to both, 5oz.; now if the cover is put on the less cup it will be double the weight of the greater cup, and put on the greater cup it will be three times as heavy as the less cup: what is the weight of each cup? Ans. 3 oz. less-4 oz. greater. 6. A person being asked, in the afternoon, what o'clock it was, answered that the time past from noon was equal to of the time to midnight; required the time ? Ans. 36 minutes past one. EXCHANGE. EXCHANGE is the paying of money in one place or country, for the like value to be received in another place or country.. There are two kinds of money, viz. Real, and Imaginary. Real money is a piece of metal coined by the authority of the State, and current at a certain price, by virtue of the said authority, or of its own intrinsic value. Imaginary money is a denomination used to express a sum of money of which there is no real species, as a litre in France, a pound in America, because there is no species current, in this or that country, precisely the value of either of the sums. Par of Exchange is the intrinsic value of the money of one country compared with that of another country, as one pound sterling is equal to thirty-five shillings Flenish. Course of exchange is the current or running price of exchange, which is sometimes above, and sometimes below par, varying according to the occurrences of trade, or demand for money. Of this course, there are tables published daily in commercial cities: thus by Lloyd's List, of 3d. December, 1799, the course of exchange between Hamburgh and London, was 32s. 6d. Flemish, per pound sterling, being 25.5ļd. under par, or loss to London. N 7 GREAT-BRITAIN. The money of account is pounds, shillings, pence and farthings. The English Guinea is 21 shillings, Sterling. Weights and measures generally as in the United States. To Change Sterling to Federal money. RULE. Annex three cyphers to the sum (if pounds only) and multiply it by 4; this product divide by 9, and you have the answer in cents. If there be shillings, &c. the usual method is to reduce it to Massachusetts money, by adding one third to it, and then reduce this sum to Federal. EXAMPLES. 1. Change £.48 Sterling to Federal. 48000 2. 9)192000 21333 cents. Ans. 213 dols. 333 cts. Change £.389 17 41Sterling to Federal,exchange at 333 per cent. that is, £.1333 Massachusetts for £.100 Sterling. 3)389 17 4 Sterling 129 19 1 Exchange Cts. ,3)519,825 173275 Federal. Ans. 1732 dols. 75cts. NOTE. Sterling is changed to Massachusetts money by adding one-third to the sum, and Massachusetts to Sterling by deducting one-fourth from it. RULE. To change Federal Currency to Sterling. |