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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 900

of $72 ; and $72--900=$.80. If $1 gains 80c., $200 will gain $200 x .80=$16, A's share. 1 300

300 x.80= 24,B's share. 1 400

400 X.80= 32,C's share. Or, we may reason thus: since the sum invested is $900, A's part of the investment is 300

2 93 3

is 300

B's 66
C's 66

900

is 400

900

OG

= 24 = 32

FA. Hence,
A must receive of $72 (the gain)=$16
B

72 С

72 PROOF.—The whole gain is $72. (Ax. 10.)

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 4 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 b of 50s., which is 21s., the answer required.

PROOF. 20 bu. X 2 js.=50s. the value of the whole mixture.

93. A miller had 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 ls. Now if i third of a bushel is taken from a bushel of rye, the remaining 2 thirds will be worth 4s.; and if I 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., and if of a bushel of wheat, which is worth 6s., be added to the rye,

the mixture will be worth 8s.; therefore, } of a bushel of rye added to { of wheat will make a mixture of 1 bushel, which is worth 8 shillings ; consequently the mixture must be } rye and f wheat; or 1 part rye to 2 parts wheat.

Proof.—Since 1 bushel of rye is worth 6s., } bu. is worth } of 6s., or 2s.; and as i bu. of wheat is worth 9s., bu. is worth of 9s., or 6s.; and 6s.+28.=8s.

Note.--If we make the difference between the less price and the price of the mixture, the numerator, and the difference between the prices of the commodities to be mixed, the denominator, the fraction will express the part to be taken of the higher priced article; and if we place the difference between the higher price and the price of the mixture over the same denominator, the fraction will express the part to be taken of the lower priced article.

94. A goldsmith has a quantity of gold 16 carats fine, and another quantity 22 carats fine'; he wishes to make a mixture 20 carats fine ; what part of each will the mixture contain. Ans. of 16 carats fine, and ĝ of 22 carats fine.

302. Examples requiring a mixture of commodities of different values, like the last three, are commonly classed under a rule called Alligation.

OBs. Alligation is usually divided into medial and alternate. The

92d example is an instance of Medial Alligation; the 93d and 94th are instances of Alternate Alligation. Questions in the latter very seldom occur in practical life.

95. A grocer mixes 50 pounds of tea worth 4 shillings a pound, with 100 lbs. worth 7s. a pound: what is a pound of the mixture worth?

96. A milk-man mixed 30 quarts of water with 120 quarts of milk, worth 5 cents per quart : what is a quart of the mixture worth ?

97. A farmer made a mixture of provender containing 30 bushels of oats, worth 25 cents per bushel ; 10 bushels of peas, worth 75 cents per bushel, and 15 bushels of corn, worth 50 cents per bushel : what is the value of the whole mixture ; and what is it worth

per

bushel ? 98. An oil dealer mixed 60 gallons of whale oil, worth 314 cents per gallon, with 85 gallons of sperm oil, worth 90 cents per gallon : what is the mixture worth per gallon?

99. A grocer had three kinds of sugar, worth 6, 8, and 12 cents per pound; he mixed 112 lbs. of the first, 150 lbs. of the second, and 175 of the third together : what was the mixture worth per pound ?

100. A goldsmith melted 10 oz. of gold 20 carats fine with 8 oz. 22 carats fine, and 4 oz. of alloy : how many carats fine was the mixture ?

101. If 4 men reap 12 acres in 2 days, how long will it take 9 men to reap 36 acres ?

Analysis.—If 4 men can reap 12 acres in 2 days, ] man can reap 4 of 12 acres in the same time, and I of 12 acres is 3 acres. Now if 1 man can reap 3 acres in 2 days, in 1 day he can reap of 3 acres, and } of 3 is 15

Again, if 1} acre requires a man 1 day, 36 acres will require him as many days as 17 is contained times in 36; and 36-1)=24 days. Now if 1 man can reap the given field in 24 days, 9 men will reap it in / of the time; and 24+9=2]. Ans. 9 men can reap 36 acres in 2 days.

acre.

Note. This and similar examples are usually placed under Compound Proportion, or “ Double Rule of Three." If the analysis of

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