CASE II. 269. When the quantity of one of the simples is given. 1. A farmer would mix rye worth 80 cents a bushel, and corn worth 75 cents a bushel, with 66 bushels of oats worth 45 cents a bushel, so that the mixture shall be worth 50 cents a bushel how much must be taken of each sort? ANALYSIS. Find the proportional parts, as in Case I: they are 11, 1 and 1. But we are to take 66 bushels of oats in the mixture; hence, each proportional number is to be taken 6 times; that is, as many times as there are units in the quotient of 6611. RULE.-I. Find the proportional numbers as in Case I, and write the given simples opposite its proportional number. II. Multiply the given simple by the ratio which its proportional number bears to each of the others, and the products will denote the quantities to be taken of each. NOTE. If we multiply the numbers in either or both of the columns C or D by any number, the proportion of the numbers in column E will be changed. Thus, if we multiply column D by 12, we shall have 60 and 12, and the numbers in column E become 66, 12 and 1, numbers which will fulfil the conditions of the question. EXAMPLES. 1. What quantity of teas at 12s. 10s. and 6s. must be mixed with 20 pounds, at 4s. a pound, to make the mixture worth 8s.. a pound? 2. How many pounds of sugar, at 7 cents and 11 cents a pound, must be mixed with 75 pounds, at 12 cents a pound, so that the mixture may be worth 10 cents a pound? 269. How do you find the proportional parts when the quantity of one simple is given ? 3. How many gallons of oil, at 7., 7s. 6d. and 9s. a gallon, must be mixed with 24 gallons of oil, at 9s. 6d. a gallon, so as to form a mixture worth 8s. a gallon? 4. Bought 10 knives at $2 each: how many must be bought at $each, that the average price of the whole shall be $14? 5. A grocer mixed with sugars worth 9 50lb. of sugar worth 10 cents a pound, cents, 74 cents, 7 cents, and 5 cents a pound, and found the mixture to be worth 8 cents a pound: how much did he take of each kind? CASE III. 270. When the quantity of the mixture is given. 1. A silversmith has four sorts of gold, viz., of 24 carats fine, of 22 carats fine, of 20 carats fine, and of 15 carats fine: he would make a mixture of 42 ounces of 17 carats fine: how much must he take of each sort? RULE.-I. Find the proportional parts as in Case I. II. Divide the quantity of the mixture by the sum of the pro portional parts, and the quotient will denote how many times each part is to be taken. Multiply this quotient by the parts separately, and each product will denote the quantity of the corresponding simple. 270. How do you find the proportional parts when the quantity of the mixture is given? NOTE. We may, as in the other cases, multiply each couplet by any number we please, which will merely change the relation of the proportional parts, and consequently give different proportions of the ingredients. Hence, there is an infinite number of answers, if we employ fractions, and often many answers to similar questions, in whole numbers.* EXAMPLES. 1. A grocer has teas at 5s., 6s., 8s., and 9s. a pound, and wishes to make a compound of 881b. worth 7s. a pound: how much of each sort must be taken? 2. A liquor dealer wishes to fill a hogshead with water, and two kinds of brandy, at $2,50 and $3,00 per gallon, so that the mixture may be worth $2,25 a gallon: in what proportions must he mix them? 3. A person sold a number of sheep, calves, and lambs, 40 in all, for $48: how many did he sell of each, if he received for each calf $13, each sheep $11, and each lamb $3? 4. A merchant sold 20 stoves for $180; for the largest size he received $20, for the middle size, $7, and for the small size 6: how many did he sell of each kind? 5. A vintner has wines at 4s., 6s., 8s., and 10s. per gallon; he wishes to make a mixture of 120 gallons, worth 5s. per gallon: what quantity must he take of each? 6. A tailor has 24 garments, worth $144. He has coats, pantaloons and vests, worth $12, $5 and $2 each, respectively: how many has he of each? 7. A jeweler melted together four sorts of gold, of 24, 22, 20 and 15 carats fine, so as to produce a compound of 42oz. of 17 carats fine: how much did he take of each sort? 8. A man paid $70 to 3 men for 35 days labor: to the first he paid $5 a day, to the second, $1 a day, and to the third, $ a day: how many days did each labor? * See an admirable article on Alligation, published by Professor D. Wood, in the June number of the New York Teacher for 1855. By his permission, I have used such parts of it as seemed appropriate to a Text Book. COINS AND CURRENCIES. 271. COINS are pieces of metal, of gold, silver, or copper, of fixed values, and impressed with a public stamp prescribed by the country where they are made. These are called specie, and are generally declared to be a legal tender in payment of debts. The Constitution of the United States provides, that gold and silver only, shall be a legal tender. The coins of a country, and those of foreign countries having a fixed value established by law, together with bank notes redeemable in specie, make up what is called the Currency. 272. A Foreign coin may be said to have four values: 1st. The intrinsic value, which is determined by the amount of pure metal which it contains : 2d. The Custom House or legal value, which is fixed by law : 3d. The mercantile value, which is the amount it will sell for in open market: 4th. The Exchange value, which is the value assigned to it in buying and selling bills of exchange between one country and another. Let us take, as an example, the English pound sterling, which is represented by the gold sovereign. Its intrinsic value, as determined at the Mint in Philadelphia, compared with our gold eagle, is $4,861. Its legal or custom house value is $4,84. Its commercial value, that is, what it will bring in Wall-street, New York, varies from $4,83 to $4,86, seldom reaching either the lowest or highest limit. The exchange value of the English pound, is $4,443, and was the legal value before the change in our standard. This change raised the legal value of the pound to $4,84, but merchants and dealers in exchange preferred to retain the old value, which became nominal, and to add the difference in the form of a premium on exchange, which is explained in Art. 287. For the values of the various coins, see TABLE, page 391. 271. What are coins? What are they called? What is declared in EXCHANGE. 273. EXCHANGE is a term which denotes the payment of money by a person residing in one place to a person residing in another. The payment is generally made by means of a bill of exchange. 274. A BILL OF EXCHANGE is an open letter of request from one person to another, desiring the payment to a third party named therein, of a certain sum of money to be paid at a specified time and place. There are always three parties to a bill of exchange, and generally four: 1. He who writes the open letter of request, is called the drawer or maker of the bill: 2. The person to whom it is directed is called the drawee: 3. The person to whom the money is ordered to be paid is called the payee; and 4. Any person who purchases a bill of exchange is called the buyer or remitter. 275. Bills of exchange are the proper money of commerce. Suppose Mr. Isaac Wilson of the city of New York, ships 1000 bags of cotton, worth £6000, to Samuel Johns & Co. of Liverpool; and at about the same time William James of New York orders goods from Liverpool, of Ambrose Spooner, to the amount of six thousand pounds sterling. Now, Mr. Wilson draws a bill of exchange on Messrs. Johns & Co. in the following form, viz. : regard to them? What is provided by the Constitution of the United States? What do you understand by Currency? 272. How many values may a coin be said to have? What is the intrinsic value? What is its Custom House value? What is the mercantile value? What is the exchange value? 273. What is Exchange? How is the payment generally made? 274. What is a Bill of Exchange? How many parties are there to a bill of exchange? Name them. 275. How do bills of exchange aid commerce? the bill in this example, Name all the parties to |