3 76. Allowing 365 days to make a year, how many years are there in 9130 days? Ans. 25 years. 77. In how many days could 63 men accomplish a piece of work which one man could do in 1000 days? Ans. 155 days. 78. Allowing a barrel to contain 196 pounds of flour, how many barrels could be filled with 4900 pounds? Ans. 25 barrels. 17 79. There being 1760 yards in a mile, find how many miles there are in 65129 yards. Ans. 37 miles. 80. How many days would 21 horses subsist on an amount of food which would suffice one horse 300 days? Ans. 14 days. 81. Allowing a steamboat to run 275 miles in a day, in what time would she make a trip of 5349 miles? Ans. 19 days. 82. A has 340 head of cattle worth 9860 dollars, and B has 760 acres of land worth 32680 dollars. Required the value of A's cattle per head, and of B's land per acre. Ans. 29 dollars; and 43 dollars. 83. Having a tract of land containing 540 acres, I wish to divide it into fields containing 45 acres each. What number of fields will it make ? Ans. 12 fields. 84. In how many days ought a company of 54 men to complete an excavation, if 75 men could do it in 150 days? Ans. 208 days. 85. A company of 100 men have provisions sufficient for 4 months. If 33 men depart from the company, how long will the same provisions suffice the remainder? After 33 men depart, 67 men will remain. The question, then, is, how long may 67 men subsist on provisions which would support 100 men for 4 months. Ans. 58 months. 86. If 27 barrels of flour be worth 135 dollars, what are 350 barrels worth, at the same price per barrel? One barrel is worth 135 dollars-27; and 350 barrels are worth 350 times as much as one barrel is worth. Ans. 1750 dollars. 87. If 39 acres of ground produce 2184 bushels of corn. how many bushels will 280 acres produce at the same rate? Ans. 15680 bushels. 88. A merchant bought 250 yards of cloth for 1750 dollars, and sold 133 yards of it at the same price at which he bought it. What did the cloth sold amount to? Ans. 931 dollars. 89. What sum of money ought a workman to earn in 503 weeks, allowing that in 297 weeks he could earn 3861 dollars? Ans. 6539 dollars. 90. A farmer has 10 head of horses, and oats enough to feed them for 5 months. If he purchase 3 more horses, how long will his oats suffice to feed the whole number? Ans. 3 months. 91. A gentleman having on hand 6975 dollars, bought 5 pair of oxen, at 45 dollars a pair, and, with the remainder of the sum, purchased 230 acres of land. What was the price of the land per acre? Ans. 29 dollars. 92. A person who undertook a journey of 1000 miles, traveled the first 7 days at the rate of 35 miles per day. How long will he be in accomplishing the remaining distance, at the rate of 33 miles per day? 80 230 Ans. 22 days. 93. A planter has 2280 dollars to lay out for mules and oxen, and wishes to purchase the same number of each. If he pay 65 dollars a head for mules, and 30 for oxen, how many of each can he buy? 65+30=95. Then 95 dollars will buy 1 mule and 1 ox; and the number of times 95 in 2280 will be the number required. Ans. 24 of each. 94. How many yards of cloth at 7 dollars a yard, 8 dollars a yard, and 9 dollars a yard,—the quantity of each kind to be the same, can a merchant buy for 1800 dollars? Ans. 75 yards of each kind. 95. A cistern, the capacity of which is 10000 gallons, is to be filled with water by 3 pipes discharging into it. The first pipe discharges 200 gallons per hour, the second and third each 150 gallons per hour. In what time will the cistern be filled by the three pipes running together? Ans. 20 hours. 96. Another cistern, the capacity of which is 15000 gallons, is supplied with water by two pipes, each discharging 325 gallons, per hour; but, by leakage, the cistern loses 100 gallons per hour. In what time would the two pipes, running together, fill the cistern? Ans. 271 hours. 97. Allowing the Moon to be 240 thousand miles from the Earth, and the Sun 95 millions of miles from the Earth; how many times the Moon's distance from us is that of the Sun ? Ans. 3950 200000 times. 350 240000 98. The velocity of light being 192 thousand 500 miles per second, and the distance from the Sun to the Earth 95 millions of miles; how many seconds does light require to pass from the Sun to the Earth? Ans. 4939500 seconds. 192500 EXERCISES ON CHAPTER II. Sign of Aggregation. § 62. A parenthesis () is used to denote the Aggregate of the inclosed expression; and this aggregate connects with whatever sign immediately precedes or follows the parenthesis. Thus (13+7)×5 denotes the sum of 13 and 7 multiplied by 5; that is, 20X5. 1. Find the value of the expression, (246+34+9+16+1)×4. 2. Find the value of the expression, 3. Find the value of the expression, 4. Find the value of the expression, 5. Find the value of the expression, Ans. 1224. Ans. 2240. Ans. 3175. Ans. 2355584. Ans. 280 6. Find the value of the expression, (4093757-307609)X(5083—3). Ans. 19233631840. 7. Find the value of the expression, (73017600-189976)÷÷÷(763+7). 8. Find the value of the expression, Ans. 94581254. (83073769+23764)X(7307—4). Ans. 606861283499. 9. Find the value of the expression, (7360793-283746+3848-500)÷÷(75013—113). Ans. 9439795 74900 10. The sum of two numbers being 35745, and one of the numbers 1740, what is the other number? Ans. 34005. 11. The difference of two numbers being 13000, and the less number 635, what is the greater number? Ans. 13635. 12. The difference of two numbers being 37073, and the greater number 739860, what is the less number? Ans. 702787. 13. The product of two numbers being 96350, and one of the numbers 470, what is the other number? Ans. 205. Two Numbers Found from their Sum and Difference. § 63. The Sum+the difference of two numbers is TWICE the greater number; and the Sum--the difference of two numbers, is TWICE the less number. For example, take the numbers 10 and 6. Their sum 16+their difference 4 is 20, which is twice 10. and their sum 16-their difference 4 is 12, which is twice 6. 14. The sum of two numbers is 80, and their difference is 20. What is the greater, and what the less number? 80+20 is 100, twice the greater; and 80-20 is 60, twice the less; hence the greater number is of 100, and the less is of 60. Ans. 50 and 30. 15. The sum of two numbers is 1000, and their difference is 200. What are the two numbers? Ans. 600 and 400. 16. The sum of two numbers being 1840, and their difference 500,-what are the two numbers? Ans. 1170 and 670. 17. The product of two numbers being 11600 and the multiplicand 80, what is the multiplier ? Ans. 145. 18. The product of two numbers being 46400, and the multiplier 240, what is the multiplicand? Ans. 193 19. The dividend being 23200, and the quotient 160, what is the divisor? The dividend is a product, and the quo. a factor. Ans. 145. 20. The sum of 1728 dollars having been divided equally among a number of men, each man received 24 dollars. What was the number of men? Ans. 72 men. 21. A and B together have 2300 dollars, and A has 500 dollars more than B. What sum has each ? Ans. A has 1400, and B 900 dollars. 22. An ironmonger bought 15 tons of iron at 39 dollars per ton, and 23 tons at 37 dollars per ton. What would he gain by selling the whole at 42 dollars per ton? Ans. 160 dollars. 23. C and D together have 4348 dollars, and C has 375 dollars less than D. What sum has each ? Ans. C has 1986, and D 2361 dollars. 24. A merchant collected from A 230 dollars, from B 303 dollars, and from C 95 dollars. If he lay out the whole sum collected, for cloth at 7 dollars a yard, how much can he buy? Ans. 89 yards. 25. A farmer wishes to fill three kinds of sacks, containing 3 bushels, 4 bushels, and 5 bushels, and the same number of each kind, with 1728 bushels of corn. How many sacks can he fill? Ans. 144 of each kind. 26. A farmer sold wheat for 900 dollars, corn for 274 dollars, and other produce for 329 dollars. Out of these proceeds he bought three pair of oxen at 55 dollars a pair, and paid the remainder for 65 acres of land. What did the land cost him per acre? Ans. 20 dollars. 27. A bought a building lot in town for 75 dollars, which was at the rate of 200 dollars per acre, and B purchased 3 pasture lots, each containing 13 acres, for 950 dollars. What quantity of ground was in A's lot, and what did B pay per acre? Ans. of an acre; and B 24 75 200 dollars. 28. If a person's income be 5000 dollars a year, and his expenses be at the rate of 5 dollars per day, at what rate would he save money per day,—there being 365 days in a year? Ans. 8 dollars per day. 29. An army of 5000 men have provisions for 3 months. If 1625 men be discharged, how long will the same provisions suffice for the remainder? 1500 Ans. 4 months. 30. A carpenter can earn 45 dollars a month, but his necessary expenditures are at the rate of 24 dollars a month. He wishes to purchase a certain lot of ground, which contains 19 acres, and is held at 35 dollars per acre. In what time can he save enough to make the purchase? Ans. 3114 months. 31. A sold to B 15 cords of wood at 3 dollars per cord, 53 barrels of corn at 2 dollars per barrel, and 2 beeves at 30 dollars each. In payment, A takes 160 dollars in cash, 3 sacks of coffee at 14 dollars a sack, and 20 gallons of molasses. What did A's sales amount to, and what did the molasses cost him per gallon? Ans. 211 dollars; and of a dollar per gallon. 20 |