297. The last and similar examples are frequently solved by a rule called Barter.

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

OBS. A specific rule for such operations seems to be worse than useless; for it burdens the memory of the learner with particular directions for the solution of questions which his common sense, if permitted to be exercised, will solve more expeditiously by the principles of analysis.

52. A shoemaker sold 6 pair of thick boots at 32 shillings a pair, and took his pay in corn at 3 shillings 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 3 shillings a pair, will it take to pay for 135 pounds of tea at 6 shillings a pound? 55. How many pounds of butter at 171⁄2 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 164 cents a pound, must be given in exchange for 256 pounds of sugar at 64 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 at 371⁄2 cents per gallon, and gave 331 pounds of cheese in exchange : how much was the cheese a pound?

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 at 87 cents apiece, for 700 grammars: how much did the grammars cost apiece?

61. What cost 680 tons of chalk at 10 shillings sterling per ton?

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

Solution. 10s.£. (Art. 147.) Now, as 1 ton costs £1,680 tons will cost 680 times as much; and 680×680÷2=£340: for multiplying by, is taking 1 half of the multiplicand once. (Art. 31.) Ans. £340.

298. Examples like the preceding one are often classed under the Rule of Practice.

Practice is defined by a late English author to be, “an abridged method of performing operations in the rule of proportion by means of aliquot parts; and it is chiefly employed in computing the prices of commodities."

OBS. After giving several tables of aliquot parts in money, weight, and measure, the same author proceeds to divide his rule into twelve subdivisions or cases, and gives a specific rule for each case, to be committed to memory by the pupil. The utility of this rule and its twelve subdivisions needs no comment.

62. What cost 720 bushels of corn at 2 shillings and 6 pence per bushel?

Solution. 2s. 6d. £. And 720×1=£90 Ans.

63. What will 560 chairs cost, at 3 of a dollar apiece? 64. What will 144 chairs cost, at of a dollar apiece? 65. What will 320 penknives cost, at of a dollar apiece?

66. What will 760 brooms cost, at of a dollar apiece? 67. At 10s. 6d. per barrel, what will 350 barrels of mackerel come to?

68. At 17s. 6d. apiece, what will 540 hats amount to? 69. If a ship cost £15000, what will of a ship cost? Solution. If a whole ship costs £15000, of one will cost times as much; and 15000 × = £11250 Ans.

70. At $20.60 per ton, what cost 12 tons and 5 hundred weight of hay?

71. What is the cost of 480 yards of ribbon, at 61 cents per yard?

72. What cost 750 bushels of potatoes, at 33 cents per bushel?

73. What cost 360 barrels of cider, at 663 cents per barrel?

74. What cost 450 chaldrons of coal, at 15s. per chaldron ?

75. What will 150 acres of land cost, at £8, 10s. per acre?

76. Three men, A, B, and C, join in an adventure; A puts in $200; B, $300; and C, $400; 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 $72-900=$.80. If $1 gains 80c.,$200 will gain $200 ×.80

900

$16,A's share.

300 ×.80

24,B's share.

Or, we may reason thus: since the sum invested is $900, A's part of the investment is 300-3;

is 300

3

900

9

299. 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 solved, is often called 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 draw 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 $400; and a third, $500; his property amounts to $800: how much 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 example seventy-sixth.

300. 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 $256.40; and C $360.40. 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 having died insolvent, it was found that he owed $55645; and his property was sold 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?

301. It often happens in storms and other casualties at sea, that masters of vessels are obliged to throw por

tions of their cargo overboard, or sacrifice the ship and their 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 D, 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.

5 bu. at 4s.=20s., value of corn.

20 bu. mixed. 50s. value of whole mixture. Now if 20 bu. mixture are worth 50s., 1 bu. is worth of 50s., which is 24s., the answer required.

PROOF. 20 bu. x2 s. 50s. the value of the whole mixture.