60 cents a pound: what is the smallest quantity of each that he can take and express the parts by whole numbers? 3. A farmer sold a number of colts at $50 each, oxen at $40, cows at $25, calves at $10, and realized an average price of $30 per head: what was the smallest number he could sell of each? 4. What is the smallest quantity of water that must be mixed with wine worth 14s. and 15s. a gallon, to form a mixture worth 13s. a gallon, when all the parts are expressed by whole numbers? CASE II. 332. 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 each opposite its simple: II. Find the ratio of the proportional number corresponding to the given simple, to the quantity of that simple to be taken, and multiply each proportional number by it. 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? 3. How many gallons of oil, at 7s., 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 $2 each, that the average price of the whole shall be $11? 5. A grocer mixed 50 lb. of sugar worth 10 cents a pound, with sugars worth 9 cents, 7 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. 333. 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? 15 + 2 + 2 + 2 = 21; 42 ÷ 21 = 2. Rule.-I. Find the proportional parts as in Case I.: II. Divide the quantity of the mixture by the sum of the proportional parts, and the quotient will denote how many times each part is to be taken. Multiply the parts separately by this quotient, and each product will denote the quantity of the corresponding simple. Examples. 1. A grocer has teas at 5s., 6s., 8s., and 9s. a pound, and wishes to make a compound of 88 lb., worth 7s. a pound: how much of each sort must be taken? 2. A liquor dealer wishes to fill a hogshead with water, and with 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 $14, and each lamb $3? 4. A merchant sold 20 stoves for $180; for the largest size he received $19 each, 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, respectvely how many has he of each ? 7. A merchant has 4 pieces of calico, each worth 24, 22, 20, and 15 cents a yard: how much must he cut from each piece to exchange for 42 yards of another piece, worth 17 cents a yard? 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? CUSTOM HOUSE BUSINESS. 334. All merchandise imported into the United States, must be landed at certain ports, called Ports of Entry. On such merchandise the General Government has imposed a greater or less tax, called a duty. 335. A PORT OF ENTRY is a port where foreign merchandise may be delivered, and where there is a Custom-house for appraisement and the payment of duties. 336. TONNAGE DUTIES are taxes levied on vessels, according to their size, for the privilege of entering ports. 337. All duties, levied by law, on imported goods, are of two kinds specific and ad valorem. : 338. SPECIFIC DUTY is a certain sum levied on a particular kind of goods named; as so much per square yard on cotton or woolen goods, so much per ton weight on iron, &c. 339. AD VALOREM DUTY is a certain rate per cent. on the invoice. 340. AN INVOICE is an inventory of goods to be landed, directed to the person who imports them, and stating their cost at the place from which they were exported. Thus, an ad valorem duty of 15% on English cloths, is a duty of 15% on the cost of the cloths imported from England. 341. The revenues of the country are under the general direction of the Secretary of the Treasury, and to secure their faithful collection, the government has appointed various officers at each port of entry, or place where goods may be landed. 342. The laws of Congress provide, that the cargoes of all vessels freighted with foreign goods or merchandise, shall be weighed or gauged by the custom-house officers at the port to which they are consigned. As duties are only to be paid on the articles, and not on the boxes, casks, and bags which contain them, certain deductions are made from the weights and measures, called Allowances. GROSS WEIGHT is the whole weight of the goods, together with that of the hogshead, barrel, box, &c., which contains them. NET WEIGHT is what remains after all deductions are made. DRAFT is an allowance from the gross weight on account of waste, where there is not actual tare. consequently, 9 lb. is the greatest draft generally allowed. TARE is an allowance made, after draft has been deducted, for the weight of the boxes, barrels, or bags containing the commodity, and is of three kinds : 1st, Legal tare, or such as is established by law; 2d, Customary tare, or such as is established by the custom among merchants; and, 3d, Actual tare, or such as is found by removing the goods and actually weighing the casks and boxes in which they are contained. On liquors in casks, customary tare is sometimes allowed on the supposition that the cask is not full, or what is called its actual wants; and then an allowance of 5 per cent. for leakage. A tare of 10 per cent. is allowed on porter, ale, and beer, in bottles, on account of breakage, and 5 per cent. on all other liquors in bottles. At the custom-house, bottles of the common size are estimated to contain 2 gallons the dozen. For tables of Tare and Duty, see Ogden on the Tariff of 1842. Examples. 1. What is the net weight of 25 hogsheads of sugar, the gross weight being 66 cwt. 3 qr. 14 lb.; tare, 11 lb. per hogshead? |