Thus 162 1. 18 s. = 3258 s. and 4 s. 6 d. = 54 d. Quest. 2. How many Saragossa Ducats, of 5 s. 6 d. the Ducat, may be had for 275 Bergonia Ducats, at 4 s. 4 d. the Piece? Answer 216 and 3 s. 8 d. over. Thus 5 s. 6d. = 66 d. and 4 s. 4 d. = 52 d. Consequently 66) 14300 (216 the Answer required. Quest. 3. A Traveller would change 2331. 16 s. 8 d. Sterling Thus 4 s. 9 d. = 57,5 d. and 233 1. 16 s. 8 d. 56120 d. Quest. 4. A Cashier hath received 759 Ducats, at 7 s. 6d. per Ducat; And 579 Dollars at 4 s. 8 d. per Dollar: Which he would exchange for Flemish Marks at 14 s. 3 d. per Piece: How many ought he to have? Answer 589 Marks, and 15 d. over. For 7 s. 6 d. 90 d. and 4 s. 8 d. = 56 d. Then {759 x 90 = 68310 d. the Value of the Ducats. 579 × 5632424 d. the Value of the Dollars. their Sum = 100734 d. And 145. 3 d. 171 d. the Flemish Mark in Pence. Quest. 5. A Bill of Exchange was accepted at London for the Payment of 400 1. Sterling, for the like Value delivered in Amfterdam, at 1 l. 13 s. 6 d. for 1 1. Sterling; How much Money was delivered at Amsterdam ? I Answer 670 l. Flemish. For 1 l. = 240 d. and 11. 135. 6 d. = 402 d. Then 240: 402:: 400: 670 the Answer required. Quest. 6. When the Exchange from Antwerp to London is at 11. 4 s. 7 d. Flemish, for I l. Sterling; How many Pounds Sterling must be paid at London; to ballance 236 1. Flemish at Antwerp. Answer 192 1. Sterling. Thus 1 l. 4 s. 7 d. = 295 d. and I l. = 240 d. Then 295: 240:: 236: 192 the Answer. P2 Quest. Quest. 7. A Merchant delivered at London 1201. Sterling to receive 147 1. Flemish in Amsterdam; How much was 11, Sterling valued at, in Flemish Money. Answer 11. 4 s. 6d. Thus 120: 147:: 240 d.: 294 d. = 1 l. 4 s. 6 d. &c. Quest. 8. A Factor hath fold Goods at Cadiz for 1468 Pieces of Eight, valued at 4 s. 6d. Sterling per Piece; How much Sterling Money do those Pieces of Eight amount to ? Answer 3331. 7 s. 2 d. Thus, if 1 = 54,5 d. then 1468 x 54,5 = 83006 d. &c. Quest. 9. A Traveller would have an equal Number of Crowns at 5 s. 6 d. per Crown; and Dollars at 4 s. 5d. per Piece; How many of each fort may he have for 3091.8 s.? Answer 624 of each. Thus 309 1. 8 s. =74256 d. Quest. 10. Suppose I would exchange 5271. 175. 6 d. for Dollars at 4 s. 6d. a Piece, Ducats at 5 s. 8 d. a Piece, and Crowns at 65. Id. a Piece; and would have 2 Dollars for 1 Ducat, and 3 Dollars for 2 Crowns. How many of each fort must I have? Answer 927 Dollars, 4631⁄2 Ducats, and 618 Crowns. And 126690 d. = 527 l. 17 s. 6 d. Now if the Crowns, Dollars, and Ducats were to be equal in Number; then 73+54+68 must have been the Divifor, by which 126690 must have been divided, and the Quotient would have been the Answer to the Question. As in the last Example. But here instead of their Sum, such Parts of them must be taken as are affigned or limited by the Question; that so the Number of fome one of them may be found. And because there must be { 2 Dollars for: Ducat, and Therefore it will be of a Ducat for one Dollar, and of a Crown for one Dollar. Confequently, Consequently, 54+:+ of 73=136, or the Divisor to find the Number of Dollars. Thus ) 126690 (927 the Number of Dollars. will be Or if you please you may form Divisors to find either the it be 2 Dollars for I Ducat, and Ducats or Crowns first: For if 3 Dollars for 2 Crowns, as before; Then will 6 Dollars be for 3 Ducats, and 6 Dollars for 4 Crowns. Therefore, Consequently, of 54: + Crown. of 68: +73=205 will be the Divifor to find the Crowns first, &c. Quest. 11. A Cashier is to receive 5001. He is offered Crowns at 6s. 1 d. per Crown, which are worth but 6.s. Or he may have Dollars at 45.5 d. the Piece, which are worth but 4 s. 4 d. Which of these shall he receive to have the least Loss? And how much will he lose in the Payment? 2 { { I Crown = 72 4.} according to the true Values. 1 Dollar = 52 d. 1 Crown = 73,5 d. I Dollar = 53,0 d. Now to find which will be the least Loss; find what the advanced Value of a Dollar ought to be in Proportion to that of I Crown. Thus 72: 73,5:: 52:53,083 &c. But he may have Dollars at 53 d. per Piece, therefore the Payment in Dollars will be the leaft Loss; viz. 53 is less than 53,083 . Next, to find what the whole Loss will be by receiving Dollars. Because the 500 l. = 120000 d. is advanced as much above the true Value, as 53d. is above 52d.: therefore say, If 53d. advance 1 d. = 53d.-52d.; what will 120000 d. advance? i. e. 53 d.: 1 d. :: 120000 d.: 2264 d. = 9 l. 8 s. 4 d. = the Lofs. Quest. 12. Suppose I exchange 41. 105. 10d. for II Crowns and 7 Dollars; and at another Time I have 4 Crowns and 3 Dollars for 11. 15 s. each being of the same Value with the first. What is the Value of a Crown, and of a Dollar? First 11 Crowns + 7 Dollars = 1090 d. } by the Question. Then in order to find the Value of I Crown, you must cast off. the Dollars by making them of the same Number; Thus, 33 Crowns+21 Dollars = 3270 d. the first multipl. with 3. 28 Crowns+21 Dollars = 2940 d. the second multipl. with 7. Then 5 Crowns = 330 d. being the Difference. Confequently 5) 330 (66=55. 6 d. is the Value of I Crown. And 4 Crowns = 264 d. Then will 3 Dollars = 420 d. - 264 d. = 156 d. Consequently 3) 156 (52 d. 45. 4 d. the Value of 1 Dollar. CHAP IX. Of Alligation. WHEN it is required to mix several Sorts of Ingredients together; as different Sorts of Corn, Wines, Wool, Spices, or Metals; or to compose Medicines, &c. the Method of proportioning fuch Mixtures, is called the Rule of Ailigation; and is divided into two Parts or Branches; called Medial and Alternate. Sect. 1. Of Alligation Pedial. Alligation Medial, is that by which the Mean Rate or Price, any Mixture is found, when the particular Quantities of the Mixtures and Rates are given; and is thus performed.. First find the Sum of all the Quantities proposed to be mixed ? And also the Sum of all their particular Rates. Rule. { Then the Proportion will be, As the Sum of all the Quantities : Is to the Sum of all their Quest. 1. Suppose 15 Bushels of Wheat at 5 s. the Bushel, and 12 Bushels of Rye at 3 s. 6 d. the Bushel, were mixed together; What 3 What is the Mean Rate or Price, it may be fold for a Bushel, without Loss or Gain? This Question prepared as directed above will stand Thus { of Wheat at 5 s. per Bushel, comes to 900 d. 12 Bushels of Rye at 3 s. 6d. each, comes to 504 d. 27 = their Sum. And their total Value = 1404 d. Then 27 Bushels: 1404 d. :: 1 Bushel: 52 d. = 4 s. 4 d. the Answer required. Quest. 2. A Grocer mixeth 36 Pounds of Tobacco, worth i's. 6 d. a Pound, with 12 Pounds of another Sort at 2 s. a Pound, and 12 Pounds of a third Sort at 1 s. 10 d. the Pound. How may he sell the Mixture per Pound? 60 the Number of Pounds. Their Value=1200 Then 60 lb : 1200 d. :: 1 lb : 20 d. = 1 s. 8 d. the Answer required. Quest. 3. A Vintner mixeth 31 Gallons and a half of Malaga Sack worth 7 s. 6 d. the Gallon; with 18 Gallons of Canary at 6 s. 9 d. the Gallon; 13 Gallons and a half of Sherry at 5 s. the Gallon; and 27 Gallons of White Wine at 4 s. 3 d. the Gallon. It is required to find what one Gallon of this Mixture is worth. 90= the Number of Gal. Their Value = 6480 Then 90: 6480 :: 1 : 72 d. = 6 s. the Rate or Price of one Gallon, as was required. The Proof of all Operations in these Sorts of Mixtures, is done by comparing the Value of all the Mixture (being fold at the Mean Rate) with the total Value of all the particular Quantities, fuppofing they had been fold at their respective Rates unmixed; if those Sums are equal, He Work is true. Sect. |