1 E. 10. Bought hofe in London, at 4s. 3d. the pair; and fold them afterwards in Dublin at 6s. the pair, now taking the charges at an average to be 2d. the pair, and confidering that I muft lofe 12 per cent. by remitting the money home again, what do I gain per cent. by this article of trade? First, 45. 3d. + 2d. — 4s. 5d. prime coft and charges. 5. d. Then, as 4 5 5. Again, 100-12-887. 1. Alfo, as 100 : 88 TEA 5 :: 13516 11:119 10 11 The amt. Subtract 100 O O Anfwer, Gained per cent. 19 10 11 XXVI. ALLIGATION MEDIAL. EACHETH how to mix or unite many fimples, or particulars, into one mafs or fum, according to any price or fum required. RULE. Multiply each quantity by its price; then say, as the fum of all the quantities, is to the fum of the faid products, fo is any part of the mixture, to the mean price of that part. PROOF. Find the value of the whole mixture, at the mean price or rate, and if it agrees with the total value of the feveral quantities at their respective prices, the work is right. EXAMPLE I. A farmer would mix 24 bufhels of wheat at 6s. per bufhel, with 40 bushels of rye at 3s. per bufhel, what will a bushel of this mixture be worth? Bush. First, 24 multiplied by its price And, 40 64 Then if 64: 264 :: 1 I by 64)264(4s. 1d. Anfwer. 256 12 4s. 1 d. 198 qrs. which mul tiplied by 64, the number of bush126724=3168d. 64)96(Id. els 12 2645. proof. E. 2. An hoftler mixed provender for his horses, viz. 18 bushels of oats at 2s. Id. per bufhel, with 16 bufhels of beans at 4s. 9d. per bufhel, and 13 bushels of malt at 35. Iod. per bufhel; I demand what a bushel of this mixture is worth? bu. d. d. 'S that by which the particular quantities of every ingrediant in any Is by which the the particular rates of every one of the ingrediants, and the mean rates, are given. RULE. 1. Place the rates of the several things one over another, and the proposed price of the compofition against them; then link the feveral rates fo together, as that one greater than the mean rate, or price of the compofition, may be coupled to a lefs; then take the differences between the mean rate and the feveral prices, and place each of them against its yoke-fellow; this being the reverse of alligation medial, may be proved thereby. EXAMPLE I. A grocer would mix fugar of 1cd. 5d. and 4d. per pound, fo that the compofition may be worth 6d. per pound, what quantity muft he take? ${ d. 10 5 4 I I } lb. d. d. Having linked the feveral rates, agreeable to the rule (whereby it is plain that these rates will admit but of one way of linking) then the difference between 6, the mean price, and 4, viz. 2, is placed againft 10, its yoke-fellow: the difference between 6 and 5 is 1, which is alfo placed against 10 its yoke-fellow; and the difference between 6 and 10 is 4, which, because it has two yoke-fellows, is placed against them both, viz. against 5 and 4; so that as oft as the grocer takes 3lb. at 10d. he must take 4 lb. of each of the other two forts to make up the mixture. Note Note. The differences are not only the quantities, which anfwer the question; but any other numbers, in the fame proportion as they are, will answer the queftion as well. E. 2. A miller hath four forts of meal, viz. one fort at 6s. 8d. another at 5s. 6d. the third at 4s. 4d. and the fourth at 35. 8d. per bufhel; but he is defirous of mixing fo much of each fort together, that he may fell it at 55. per bufhel; how much of each fort must he take? Note. Examples of this nature will admit of as many answers as there are different ways of linking together a larger price and a leffer than the mean rate proposed. Is XXVIII. ALLIGATION PARTIAL. S when the particular rates, the mean rate, and the quantity of one ingredient, is given, to find the quantity of all the rest of the ingredients. This is called alligation partial, because a part of the mixed ingredients only are given. RULE. 1. Take the difference between each price and the mean rate, as in the last rule. 2. As the difference oppofite to the known quantity, is to the known given quantity; fo is any other difference, to the quantity of its oppofite name. EXAMPLE I. A farmer being determined to mix 12 bushels of wheat at 6s. per bushel, with rye at 4s. barley at 35. and oats at 2s. 6d. per bufhel; I demand how much rye, barley and oats, must be mixed with the faid 12 bufhels of wheat, fo that the whole may be fold for 3s. 6d. bufhel? per All examples belonging to this and the following rule, may be proved by the rule in alligation medial. Note. A compofition made of 6 bufhels of wheat at 72d. per bufhel, 12 of rye at 48d.30 of barley at 36d. and 6 of oats at 30d. per bufhel, will bear the mean price of 42d. or 3s. 6d. per bushel; you must obferve, that in this compofition there are only 6 bushels of wheat, but the demand is 12 bufhels; therefore the proportion above is found thus: As the difference annexed to the branch, is to the other particular differences, fo is the given quantity to the feveral quantities required. To find how much rye, barley and oats must be mixed with the 12 bufhels of wheat, fay, if 6 bufhels of wheat require 12 bufhels of rye, what will 12 bushels of wheat require? Answer, 24 bufhels of rye. And by proceeding in like manner with the other mixtures, you will find their respective proportions as in the preceding work. E. 2. A tobacconist has by him 120 lbs of Oroonoko tobacco, worth 2s. 6d. a pound; to this he would mix York-River ditto at zod. and other inferior tobacco at 18d. and 15d. a pound, as will make up a mixture answerable to 23. a pound; what will this parcel weigh? Diff. lb. diff. E. 3. What quantity of gold, at 15, 16, and 18 caracts fine, muft be mixed with 80 ounces of pure gold, viz. fuch as is 24 caracts fine, so that the compofition may be 20 caracts fine? 11)320(29oz.of 18,15,and 16 caracts fine, Anf. Is XXIX. ALLIGATION TOTAL. [S when the price of each fimple is given, alfo the mean rate and quantity of the compound, to find how much of each fort will make that quantity. RULE. Say, as the fum of the differences, to the quantity given, fo is every particular difference, to its respective quantity. EXAMPLE 1. A brewer hath three forts of beer, viz. at 9d. 13d. and 18d. per gallon, which he would mix together, and the whole mixture to contain 60 gallons; how much of each fort must be taken that the mixture may be worth 10d. per gallon? gall. d. gall. d. PROOF. As 60: 614 the value of the whole mixture :: I : 10 the mean price given. E. 2. A mixture of wine is to be made up, confifting of 130 quarts, from these five forts, whofe prices are 7d. 8d. 10d. 14d. and 15d. a quart; and the whole is to be fold at 127. per quart; how much of each fort must be taken? |