51. A merchant sold 22 yards of silk, at 7 shillings per yard, and took his pay in wheat, at 11 shillings per bushel: how many bushels did it take?

7s.

22

11)154s.

Suggestion.-We first find the cost of the silk, Operation. which is 154s. The next step is to find how many bushels of wheat it will take to pay this 154s. Now as the wheat is 11s. a bushel, it will evidently take as many bushels as 11s. are contained times in 154s., which is 14. Therefore it will take 14 bu. of wheat, at 11s. per bu., to pay for 22 yds. of silk, at 7s. per yard.

Ans. 14 bu.

297. The last and similar examples are sometimes placed under a rule called Barter.

Barter signifies an exchange of articles of commerce, at prices agreed upon by the parties.

OBS Such examples are so easily solved by Analysis, foat a specific rule for them is unnecessary.

52. A shoemaker sold 64 pair of boots at 32s. 6d. a pair, and took his pay in corn at 3s. 4d. per bushel: how many bushels did he receive?

53. A man bought 50 pounds of sugar at 12 cents a pound, and was to pay for it in wood at $3.12 per cord: how many cords did it take?

54. How many pair of hose, at 3s. 9d. a pair, will it take to pay for 135 pounds of tea at 6s. 4d. a pound?

55. How many pounds of butter at 17 cents a pound, must be given in exchange for 186 yards of calico at 183 cents per yard?

56. How many pounds of tobacco at 16 cents a pound, must be given in exchange for 256 pounds of sugar at 61 cents a pound?

57. A farmer bought 325 sheep at $21 apiece, and paid for them in hay at $10 per ton: how many tons did it take ?

58. A man bought a hogshead of molasses worth 371⁄2 cents per gallon, and gave 3311⁄2 pounds of cheese in exchange: how nuch was the cheese a pound?

QUEST.-297. What is meant by Barter? Obs. Is a specific rule necessary for Buch operations ?

59. Bought 74 bushels of salt at 42 cents per bushel, and paid in oats at of a dollar per bushel: how many oats did it require?

60. A bookseller exchanges 400 dictionaries worth 871 cents apiece, for 700 grammars: how much did the grammars cost apieee?

61. How many yards of silk worth $12 per yard, will pay for 249 yards of cloth worth $5 per yard?

62. Bought 19 cwt. 2 qrs. 15 lbs. of sugar at $9 per hundred, and paid for it in butter at 71 cents a pound: how much butter did it take?

63. Bought 263 yds. 3 qrs. of satinet at $13 per yard, and paid for it in cheese at $9 per hundred: how much cheese did it take?

64. Bought 125 hhds. 22 gals. 3 qts. of molasses at 371 cents per gallon, and paid for it in wool at 62 cents a pound: how much wool did it take?

65. Bought .778125 ton of indigo at $4 a pound: how much cloth at $57 per yard will pay for it?

66. Bought .45683 acre of land at $3 per square foot: how many cords of wood did it require at $33 per cord to pay for it? 67. How many barrels of flour at $6 per barrel, must be given in exchange for 45 tons, 15 cwt. 20 lbs. of coal, at $7 per ton?

68. A goldsmith sold a tankard for £12, 8s., which was 5s. 4d. per ounce, and agreed to take as many yards of silk as there were ounces in the tankard: how many yards did he receive?

69. Bought 432 sheep at $21 apiece, for which I paid 144 barrels of flour: what was the flour per barrel ?

70. If 15 yards of domestic flannel are worth 25 yards of muslin, how many yards of flannel are worth 15 yards of muslin ?

71. A market-woman bought 10 dozen oranges at the rate of 3 for 4 cents, and then exchanged them for eggs at the rate of 4 for 5 cents: how many eggs did she receive?

72. If 15 lbs. of pepper are worth 25 lbs. of ginger, how many pounds of ginger must be given for 195 lbs. of pepper? 73. If 11 boys can earn as much as 5 men, how many boys can earn as much as 145 men?

74. How much cotton at $7.50 per hundred, must be given for 175 tons, 10 cwt. 15 lbs. of flour, at $2.25 per hundred?

75. How much soap at 10 cents a pound, must be given for 17 cwt. 10 lbs. of potash at 6} cents a pound?

76. Three men, A, B, and C join in an adventure; A puts in $200; B, $300; and C, $100; and they gain $72: how much is each man's share of the gain?

Analysis—The whole sum invested is $200+ $300+$400= $900. Now, since $900 gain $72, $1 will gain of $72; and $72÷900 $.08. Again,

If $1 gains Sc., $200 will gain $200 × .08=$16, A's share.

Or, we may reason thus: since the sum invested is $900, A's part of the investment is, which is equal to &;

A must therefore receive & of $72 (the gain)=$16

20 30 40

298. When two or more individuals associate themselves together for the purpose of carrying on a joint business, the union is called a partnership or copartnership.

OBS. The process by which examples like the last one are commonly solved, is called Partnership, or Fellowship.

77. A and B entered into partnership; A furnished $400, and B $500; they gained $300: how much was each man's share of the gain?

78. A, B, and C hired a farm together, for which they paid $175 rent; A advanced $75; B, $60; and C, $40. They raised 250 bushels of wheat: what was each man's share?

79. A, B, and C together spent $1000 in lottery tickets. A put in $400; B, $250; and C, $350; they drew a prize of $1500: how much was each man's share?

80. A, B, C, and D fitted out a whale ship; A advanced $10000; B, $12000; C, $15000; and D, $8000; the ship brought home 3000 bbls. of oil: what was each man's share?

81. A, B, and C formed a partnership; A furnished $900; B, $1500; and C, $1200; they lost $1260: what was each man's share of the loss?

82. X, Y, and Z entered into a joint speculation, on a capital of $20000, of which X furnished $5000; Y, $7000; and Z the balance; their net profits were $5000 per annum: what was the share of each?

83. A bankrupt owes one of his creditors $300; another $100; and a third $500; his property amounts to $800: how inuch can he pay on a dollar; and how much will each of his creditors receive?

Note. The solution of this example is the same in principle as that of example seventy-sixth.

299. A bankrupt is a person who is insolvent, or unable to pay his just debts.

OBS. Examples like the preceding one are sometimes arranged under a rule called Bankruptcy.

84. A bankrupt owes $2000, and his property is appraised at $1600: how much can he pay on a dollar?

85. A man failing in business, owes A $156.45; B $256.46; and C $360.40; and his effects are valued at $317: how much will each man receive?

86. The whole effects of a man failing in business amounted to $3560, he owed $35600: how much can he pay on a dollar; and how much will B receive, who has a claim on him of $5000?

87. A man died insolvent, owing $55645; and his property was sold at auction for $2350: how much will his estate pay on a dollar?

88. How much can a bankrupt, who has $6540 real estate, and owes $56000, pay on a dollar?

300. It often happens in storms and other casualties at sea, that masters of vessels are obliged to throw portions of their cargo overboard, or sacrifice their ship and crew. In such cases, the law requires that the loss shall be divided among the owners of the vessel and cargo, in proportion to the amount of each one's property at stake.

The process of finding each man's loss, in such instances, is called General Average.

OBS. The operation is the same as that in solving questions in bankruptcy and partnership.

89. A, B, and C freighted a sloop with flour from New York to Boston; A had on board 600 barrels; B, 400; and C, 200. On her passage 200 barrels were thrown overboard in a gale, and the loss was shared among the owners according to the quantity of flour each had on board: what was the loss of each ?

90. A Liverpool packet being in distress, the master threw goods overboard to the amount of $10000. The whole cargo was valued at $72000, and the ship at $28000: what per cent. loss was the general average; and how much was A's loss, who had goods aboard to the amount of $15000?

91. A coasting vessel being overtaken in a gale, the master was obliged to throw overboard part of his cargo, valued at $15500. The whole cargo was worth $85265, and the vessel $17000: what per cent. was the general average; and what was the loss of the master, who owned of the vessel?

92. A farmer mixed 15 bushels of oats worth 2 shillings per bushel, with 5 bushels of corn worth 4 shillings per bushel: what is the mixture worth per bushel?

Solution.-15 bu. at 2s.=30s., value of oats.

20 bu. mixed 50s., value of whole mixture.

Now, if 20 bu. mixture are worth 50s., 1 bu. is worth of 30s., which is 21s., the answer required.

PROOF.-20 bu. x 21s. 50s. the value of the whole mixture.

93. A miller has a quantity of rye worth 6s. per bushel, and wheat worth 9s. per bushel; he wishes to make a mixture of them which shall be worth 8s. per bushel: what part of each must the mixture contain?

Analysis.-The difference in their prices per bushel is 3s.; hence, the difference in the price of 1 third of a bushel of each is 1s. Now, if 1 third of a bushel is taken from a bushel of rye, the remaining 2 thirds will be worth 4s.; and if 1 third of a bushel of wheat, which is worth 3s., be added to the rye, the mixture will be worth 7s. Again, if of a bushel is taken from a bushel of rye, the remaining third will be worth 2s.,