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77. If the interest of $100 for 1 year be $6, what will be the interest of the same sum for 4 years ? For 6 years ? For 6 months (or 1 a year)? For 1 month (or 30 days) ? For 2 days ? For 15 days?
Ans. to the last, $0*25. 78. If the interest of $100 for 1 year be $6, what will be the interest of $1 for the same time? Of $145 ? Of $27.50 ? Of $1472 ? Of $562 ? Of $25.25 ? Of $304 ?
Ans. to the last, $18.24. 79. If the interest of $109 be $7 for 1 year, what will be the interest of $325 for the same time? Of $62-50 ? Of $235 ?
Ans. to the last, $16.45. 80. If the interest of $350 for 1 year be $1750, in what time will the interest on the same sum be $87650 ? Be $7875 ? Be $91.875 ?
Ans. to the last, 54 yrs. 81. What is the interest of $100 for 1 year, when the interest of $1750 for 4 years is $350 ? Is $280 ? Is $560 ?
Ans, to the last, $8.
Partnership. 82. Three men, A, B, and C, trade in company, and agree to share the profits in proportion to the amount of property each furnishes to the common stock? A puts in $2000, B $4000, and C $6000. They gain $3000. What is each man's share of the gain? Observe that $3000 is gained by trading with $12,000. What is the gain for every dollar put in ? Prove by the sum of the gains.
83. A, B, C, and D, are concerned in a joint stock of $1000, of which A's part is $150, B's $250, C's 275, and D's 325. On the adjustment of their accounts, they find they have lost $337-50. What is the loss of each partner ?
Suggestive Questions.—What is the loss on each dollar of stock? Then what is each man's several loss? Prove by addition of the several losses.
84. A ship, worth $3000, being lost at sea, of which belonged to A, i to B, and the rest to C, what loss will each sustain, supposing $450 to have been insured on her ?
Suggestive Questions.- What is the whole loss? What part of the vessel belonged to C? What was each man's loss ? Prove by taking the sum of the insurance and of the several losses.
85. A, B, and C, freighted a ship with 68,900 feet of boards. A put in 16,520 feet, B 28,720, and C the rest. In
a storm, 13,780 feet were thrown overboard to lighten the vessel. How many feet had C ? What loss would be sustained on every foot of boards? How many feet would each individual lose? Prove as before.
86. A and B, venturing equal sums of money, cleared by joint trade $273. By agreement, as A executed the business, he was to have 8 per cent., and B 5 per cent. How much was A allowed for his trouble ?
Suggestive Questions.-Out of every $8 that A had, how much was for his trouble in doing the business? How many 13s in 273? How many times, then, had he 3 dollars for his trouble ? Prove as before.
87. In a profitable transaction, A and B were partners. A put in $45, and took of the gain? What did B put in ?
Suggestive Questions.—If A took of the gain, what proportion of the capital must he have advanced ? Then what proportion must B have advanced ? If $45 was of the capital, what is } ? ? Prove. 88. A, B, and C, put $720 in a partnership concern,
and gained $540, of which, as often as A took $3, B took $5, and C $7. What did each advance, and what did each gain ?
Suggestive Questions. As their profits were divided according to their advances, for every $15 advanced A paid $3. Then how many 15s in $720 ? Prove.
89. A bankrupt is indebted to A $120, to B $230, to C $340, to D $450; and his whole estate amounts only to $560. How must it be divided among his cre tors, or, which is the same thing, how much will each receive for every dollar due ? Prove as before.
90. Divide 360 into four such parts as shall be to each other in the proportion of 3, 4, 5, 6; that is, every time the first has 3, the second shall have 4, &c. Prove by addition.
91. Divide $540 into four parts, bearing to each other the proportion of }, d, 4, and to, and prove by addition.
92. The taxes in a certain town amount to $4000. It contains taxable property to the amount of $125,000, and 500 polls (that is, individuals who are personally taxed), who pay 50 cents each. What part of the tax was laid on property ? What was the tax on every dollar? What was the amount of A's tax, whose list is $1400 and 1 poll; B's, whose list is $1200 and 2 polls; and C's, whose list is $400 and 1 poll?
and how much did the remainder of the town contribute for polls and for property ? Prove by addition.
93. Four farmers hire a pasture for $75. A puts in 75 sheep for 16 weeks; B 50 for 24 weeks ; C 120 for 20 weeks; and D 50 for 4 weeks. How much does it cost them per week for each sheep, and how much has each to pay towards the rent? Prove by addition.
94. Three farmers hire a pasture. A puts in 80 sheep for 4 months; B 60 sheep for 2 months; C pays $2160 towards the rent, and puts in 72 sheep for 5 months. What was the whole rent of the pasture, and what share did A and B severally pay? Prove.
95. Four merchants traded in company. A put in $400 for 5 months; B $600 for 7 months; C $960 for 8 months ; and D 1200 for 9 months. By misfortunes at sea they lost $617. . What must each man sustain of the loss?
Suggestion.—$400 for 5 months is equal to $100 for how many months ? Prove.
96. A, with a capital of £100, began trade Jan. 1, 1850. He took in B as a partner on the first day of March following, with a capital of £150; and, three months afterwards, they admitted C as a third partner, who brought into the business £180. After trading together till the first of Jan., 1851, they found there had been gained since A's commencing business £264. How must this be divided among the partners ? Prove.
97. Suppose the gain mentioned in the last question had been from the time of C's entering into partnership, how should it be divided then? Prove.
98. A merchant, A, commences business on the first of Jan., with a capital of $3000. He takes B into partnership on April 1, and C on July 1. Their profits were $2400, which were to be divided in proportion to the amount of capital furnished by each, and the length of time it was used. It so happened that each received }, or $800. How much capital did B and C severally furnish?
Exchange. 99. How much New York currency is equal to £150 of Canada currency ? See table of Provincial Currencies, p. 227, and examples, p. 248. See, atso, p. viii.
100. How much Canada currency will pay a debt of £240 in New York ?
101. How many dollars will pay a debt of £77 16s. 8d. in Charleston, South Carolina ?
102. How much of South Carolina currency can be cancelled by $3334 ?
103. What sum in New England currency will cancel a debt of £93 18s. 6d. in Fayetteville, North Carolina ?
104. What sum in North Carolina or New York currency will cancel a debt of £70 8s. 10 d. in New England ?
105. A traveller wishes to change £233 16s. 8d. sterling for Venice ducats, at 4s. 9 d. per ducat. How many
ducats must he have ?
Mean Numbers and Values, commonly called Alligation.
106. A merchant mixes 8 lbs. of tea worth 35 cts. per pound, with 24 lbs. worth 44 cts. per pound. What is the value of the whole mixture ? and what is the mean value, or value of the mixture per pound ?
Ans. to the last question, 41 cts. 107. A farmer mixes 18 bushels of corn, worth 75 cts. per bushel, with 9 bushels of oats, at 33} cts. per bushel, and 4 bushels of bran, at 15 cts. per bushel. What is the value of the whole mixture, and how much its mean value per
bushel ? Prove as below.
108. The same man makes another mixture of 4 bushels of rye, at 60 cents per bushel ; 15 bushels of buckwheat, at 40 cts. ; and 8 bushels of corn, at 75 cts. per bushel. What is the mean value of the mixture per bushel ? Prove as above.
109. A grocer bought 3 barrels of sugar; one at 5 cts. per Ib., one at 6, and one at 7 cts. per lb. What is the average or mean value of the whole, supposing each barrel to contain the same weight of sugar ? Prove.
110. A goldsmith melts together 4 lbs. of gold, of 22 carats fine; 1 lb., of 20 carats fine; and 1 lb., of 16 carats fine. What is the fineness of the mixture; that is, the mean number of carats of fineness? Prove.
The fineness of gold is estimated by carats. Pure gold
is 24 carats fine. The smaller the number of carats, the less pure is the metal.
111. The average or mean height of the thermometer at a certain place for the month of December was 30 degrees; the average for January was 27°; and the average for February was 24o. What was the average height for the three months?
Ans. 27°. 112. A merchant wishes to mix coffee, at 10 cts. and 14 cts. per pound, so that the compound shall be worth 12 cts. per pound. Should the quantities of the two sorts be equal or unequal ?
Suggestive Questions.—How much does the price of the least costly fall short of the price of the mixture ? How much does the price of the most costly exceed that of the mixture ? Will the gain on 1 lb. of the former, then, exactly balance the loss on 1 lb. of the latter ? Should the quantities of the two sorts, then, be equal or unequal ?
113. What proportions of coffee at the following prices, namely, at 6 cts., 7 cts., 10 cts., and 12 cts., per lb., should be mixed so as to make a compound worth 9 cts. per lb. ?
19 at 9=81
Suggestive Questions. If the mixture is to be sold at 9 cts. per lb., what will be the gain on each pound of the 6 cent? What will be the loss on each lb. at 10 cents? Then how many lbs. should go into the mixture of that losing 1 cent, to balance the 1 lb. which gains 3? Will 1 lb. at 6 cents, then, exactly balance 3 lbs. at 10 ? Mark the quantities, then, 1 and 3, in the blank column, opposite 6 and 10. Compare the two quantities you have just written, and say why the quantities are in inverse order to the differences in price from the mixture. Will a greater difference always require a less quantity, and a less difference require a greater quantity ? Balance the prices, 7 and 12, in the same manner, avoiding fractions by doubling, or trebling, &c., both numbers. One ib. at 12 will