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63. A man driving some oxen, some cows, and some sheep, being asked how many he had of each sort, an'swered, that he had twice as many sheep as cows, and three times as many cows as oxen; and that the whole number was 80. What was the number of each sort?
64. A man has a note of $ 647. due in 2 years and 7 months without interest; but being in want of money, he will sell the note; what ought he to receive, when interest is 6 per cent. a year ?
65. A gentleman bequeathed an estate of $12500. to his wife and son. The son's share was of the wife's share. What was the share of each ?
66. A man and his wife found that when they were together, a bushel of corn would last them 15 days; but when the man was absent, it would last the woman alone 27 days. How long would it last the man alone ?
67. A farmer sold some calves and some sheep for $108.; the calves at $5. and the sheep at $8. apiece. » There were twice as many calves as sheep. What was the number of each sort?
68. A owes B $ 158.33 due in 11 months and 17 days, without interest, which be proposes to pay at present. What ought he to pay, money being 5 per cent. ?
69. At what time, between twelve and one o'clock, do the hour and minute hands of a clock or watch point in directions exactly opposite ?
70. If 3 men can do a piece of work in 56 days, and 4 women can do the same in the same time, in what time will one man and one woman together perform it ?
71. A son having asked his father's age, the father thus replied; your age is 12 years, to which if fiveeighths of both our ages be added, the sum will express my age.' What was the father's age ?
72. Three gentlemen agree to contribute $730. towards the building of a church at the distance of 2 miles from the first, 27 miles from the second, and 31 miles from the third; and they agree, that their shares shall be reciprocally proportional to their distances from the church. How much must each contribute ?
73. If A can reap a field in 13 days, and B in 16 days, in what time can both together reap it?
74. A and B set out together from the same place, and travelled in the same direction. A travelled uniformly 18 miles a day, but after 9 days turned and went back as far as B had travelled during those 9 days; he then turned again, and, pursuing his journey, overtook B in 22į days from the time they first set out. At what rate per day did B uniformly travel ?
75. Two men, A and B, are on a straight road, on the opposite sides of a gate; A is distant from it 308 yards, and B 277 yards, travelling each towards the gate. How long must they walk, to make their distances from the gate equal; allowing A to walk 2} yards, and B 2 yards, per second ?
76. I want just an acre of land cut off from the end of a piece, which is 13, rods wide; how much of the length of the piece will it take?
77. A farmer had oats at 38 cents a bushel, which he mixed with corn at 75 cents a bushel, so that the mixture might be 50 cents a bushel. What were the proportions of the mixture ?
78. A grocer mixed 123lb. of sugar worth 8 cents per lb. with 87 lb. worth 11 cents per lb. and 15 lb. worth 13 cents per lb. What was the mixture worth per lb. ?
79. A. man travelling from Boston to Philadelphia, a distance of 335 miles, at the expiration of 7 days found that the distance which he had to travel was equal to 25 of the distance, which he had already travelled. How many miles per day did he travel ?
80. A gentleman bequeathed an estate of $ 50000. to his wife, son, and daughter; to his wife he gave $ 1500. more than to the son, and to his son $ 3500. more than to his daughter. How much was the share of each ?
81. The stock of a cotton manufactory is divided into 32 shares, and owned equally by 8 persons, A, B, C, &c. A sells 3 of his shares to a ninth person, who thus becomes a member of the company, and B sells 2 of his shares to the company, who pay for them from the common stock. After this, what proportion of the whole stock does A own?
82. How many feet in a stock of 18 boards, 12 feet 3 inches long, and 1 foot 8 inches wide ?
83. A merchant laid out $ 50. for linen and cotton cloth, buying 3 yards of linen for a dollar, and 5 yards of cotton for a dollar. He afterwards sold i of his linen and } of his cotton for $12, which was 60 cents more than it cost him. How much of each did he buy?
84. If 157 dollars 50 cents in 16 months gain 12 dollars 60 cents, in what time will 293 dollars 75 cents gain 11 dollars 75 cents, at the same rate of interest ?
85. A merchant having goat-skins, and wishing to get ! some of them dressed, delivered for that purpose 560 to a currier, to be dressed at 12 cents each, who agreed to take his pay in dressed skins at 50 cents each. How many dressed skins should the currier return?
86. If eggs be bought at the rate of 5 for 4 cents, how must they be sold per dozen, to gain 25 per cent. ?
87. What is the circumference of a wheel, the diameter of which is 5 feet ?
88. A lion of bronze, placed upon the basin of a fountain, can spout water into the basin through his throat, his eyes, and his right foot. If he spouts through his throat only, he will fill the basin in 6 hours; if through his right eye only, he will fill it in 2 days; if through his. left eye only, in 3 days; if through his foot only, he will fill it in 4 hours. In what time will the basin be filled, if the water flow through all the apertures at once ?
89. A man having 100 dollars spent part of it, and afterward received five times as much as he had spent, and then his money was double what it was at first. How much did he spend ?
90. A hare starts 50 leaps before a grey-hound, and takes 4 leaps to the hound's 3; but 2 of the hound's leaps are equal to 3 of the hare's. How many leaps must the hound make, to overtake the hare ?
91. A grocer would mix the following kinds of sugar, viz. at 10 cents, 13 cents, and 16 cents per lb. What quantity of each must he take, to make a mixture worth 12 cents per lb. ?
92. A grocer has 43 gallons of wine worth $1.75 a gallon, which he wishes to mix with another kind worth $ 1.40 a gallon, in such proportion that the mixture may
be worth $1.60 a gallon. How many gallons at $1.40 must he use?
93. Three merchants, A, B, and C, freight a ship with wine. A puts on board 500 tons, B 340 tons, and C 94 tons; and in a storm they are obliged to cast 150 tons overboard. What loss does each sustain ?
94. A and B hired a pasture for 37 dollars. A put in 3 horses for 4 months, and B 5 horses for 3 months. What ought each to pay?
95. A family of 10 persons took a large house for 1 of a year, for which they agreed to pay 500 dollars for that time. At the end of 14 weeks, they took in 4 new lodgers; and after 3 weeks, 4 more; and so on at the end of every 3 weeks, during the term, they took in 4 more. How much rent must one of each class pay?
96. A boy bought 12 apples and 6 pears for 17 cents, and then, at the same rate, 3 apples and 12 pears for 20 cents. What was the price of an apple, and of a pear ?
97. A certain square pavement contains 45941 square stones, all of the same size. How many stones constitute the length of one side of the pavement?
98. A certain field lies in the form of a right-angled triangle; the sides containing the right angle are, one 48 rods, the other 20 rods in length. What is the length of the other side ? How many acres in the field ?
99. The following lots of sugar, from Havana, were sold in Boston on account of owners in Cuba, at 123 cents per lb. Required the amount of sales for each owner, allowing draft 4 lb. per box, and tare 15 per cent.
A's sugar, 21 boxes, weighing 10794 lb. gross.
D's sugar, 105 boxes, weighing 53970lb. gross. 100. How much money on interest at the rate of 6 per cent. a year, from February 16th 1835, will be sufficient to meet a custom-house bond of $ 1464.45, which will become due on 10th of January, 1836 ?
101. How many shingles will cover the roof of a house, which is 40 feet in length, and has 30 feet rafters, supposing each shingle to be 4 inches wide, and each course to be 6 inches ?
102. A merchant sold a piece of cloth for $ 40, and by so doing, lost 10 per cent. For how much should he have sold it, to have gained 15 per cent.?
103. A merchant received on consignment, three parcels of hops, viz. 450 lb. from Allen, 890 lb. from Brooks, and 5101h. from Chase, Allen's hops were found on inspection to be 33} per cent. better than the others, but it was necessary to sell them together, at 12 cts. a pound. How much must each owner be credited ?
104. Three parcels of beef, of 60 barrels each, were received at Baltimore, from Boston, marked, W, X, Y. The lot marked W was found to be.50 per cent. better than the others. The whole was sold together at 10 dollars a barrel. How must the sale be adjusted between the owners of the beef ?
105. If iron worth $4, per cwt. cash, is sold for $4.50, on a credit of 8 months, what credit should be allowed on wine worth in cash $ 224 per pipe, but sold at $ 242, to make the percentage equal to that on the iron ?
106. The number of terms in an equidifferent series is 11, the last term is 32, and the sum of the terms is 187. Find the first term, and the common difference.
107. Amerchant has three notes, due to him as follows; one of $ 300, due in 2 months; one of $ 250, due in 5 months; and one of $ 180, due 3 months ago, with interest; the whole of which he now receives. What sum is received on the three notes, allowing money to be worth 6 per cent. a year ?
109. A lady has two silver cups, and only one cover. The first cup weighs 12 oz. If the first cup be covered, it will weigh twice as much as the second; but if the second cup be covered, it will weigh three times as much as the first. What is the weight of the cover, and of the second cup ?
109. Gray of Baltimore remits to Degrand in Boston, for sale, a set of exchange on London, the proceeds of which to be invested in certain merchandise for Gray's account. On selling the bill at 10 per cent. advance, D received $8600. How many pounds sterling was the bill drawn for, and how much is D to lay out for G, re