117. Miscellaneous Examples. 15. A merchant bought goods for $ 1084, and sold them for $ 594 more than he gave. How much did he receive for them ? 16. From a farm containing 984 acres there were sold at one time 347 acres, at another time 157 acres. How many acres remained ? 17. A merchant bought goods for $2467, and sold them for $ 875 less than he gave. How much did he receive for them ? 18. If I take 7642 gallons from 21002 gallons twice, what will remain ? 19. Of 30070 men who went into battle, 4564 were slain and 1675 were taken prisoners. How many were left ? 20. Bought two horses; the first cost $215, the second $40 less than the first. How much did the two horses cost ? 21. If $ 19.74 were paid for 14 bushels of wheat, what must be paid for 25 bushels ? 22. If 19 tons of coal run an engine 798 miles, how far will 14 tons run it? 23. The area of the New England States is as follows: Maine, 31766 square miles; New Hampshire, 9280; Vermont, 10212; Massachusetts, 7800; Connecticut, 4674; Rhode Island, 1306. How many more square miles are there in Maine than in the three States of Vermont, New Hampshire, and Massachusetts ? 24. How many States of the size of Rhode Island might be made out of Massachusetts, and how many square miles would remain ? 25. How much smaller is Connecticut than Vermont? square many States of the size of New England might be made out of it, and how many States of the size of New Hampshire out of the remainder? 27. If 5 bushels of wheat of 60 pounds each are required to make 1 barrel of flour, how many pounds of wheat are required to make 100 barrels of flour ? 28. In a certain schoolhouse 9 of the rooms will seat 52 pupils each, and 4 will seat 48 pupils each. How many pupils can be seated in all ? 29. How many feet of fencing will be required to enclose a lot of land measuring on each of two sides 489 feet, on the third 548 feet, and on the fourth 596 feet ? 30. In a school there are 7 classes of 54 pupils each; 196 of these are boys. How many are girls ? 31. A horse cost $ 262, a chaise $ 228, and a hack 3 times as much as both. What did all cost ? 32. A farmer exchanged 4 cows, worth $ 68 each, for a span of horses. What were the horses worth apiece ? 33. A merchant bought 45 bales of cotton, each bale containing 42 pieces, and each piece 38 yards, at 9 cents a yard, and sold the whole at 11 cents a yard. How much did he gain ? 34. A man raised in one year 364 bushels of corn, the next year twice as much as he did the first year, and the third year three times as much as the second year. How many bushels did he raise in all ? 35. A grocer bought 8 chests of tea, each chest containing 48 pounds, at 50 cents a pound. He sold one half of the tea at 65 cents a pound and the other half at 72 cents a pound. How much did he gain ? 36. After $ 158 were taken from a box there remained $ 15 more than twice that sum. How many dollars remained ? 37. Mrs. Keyes, having $2000 to invest, bought 10 United States bonds at $ 112 each, and then as many railroad shares at $ 92 each as she could pay for. How much money was left ? 38. Mr. Oaks bought a piano for $375, paid $ 14 for freight and cartage, and $2 for tuning, then let it 7 quarters at $15 a quarter, and afterwards sold it for $325. Did he gain or lose, and how much ? 39. A man paid $ 270 for a threshing-machine, and hired help to run it at $5 a day. He then let the machine at $8 a day, including the help he hired. How many days must he let the machine to pay its first cost ? 40. How many posts and how many rails will be required for a fence 156 feet long if the posts are set 12 feet apart and the fonce is 5 rails high ? 41. A man sold three houses; for the first he received $3525, for the second $ 950 less than he received for the first, and for the third as much as for the other two. How much did he receive for the three ? 42. A jeweller sold 15 clocks and 22 watches; for the clocks he received $ 12 apiece, and for each watch 7 times as much as for a clock. What did he receive for all ? 43. If 28 men can grade a road in 72 days, how long will it take 36 men to do half the work ? 44. If a man earns $150 a month and spends $ 36 for board and $ 50 for clothes and other expenses, in how many months can he save $ 1410 ? 45. Mr. Brown bought 18 cords of wood for $110. For how much must he sell it a cord to gain $ 34 on the whole ? 46. Mr. Snow bought some land for $ 13825. He sold 100 acres at $ 55 an acre, and then found, in order not to lose on his bargain, that he must sell the remainder for $ 62 an acre. How many acres were there in the remainder ? 47. A had $ 45; B twice as much less $17; and C as much as A and B together. How much money haul C? 48. One half of one number is 1764, and four times another number is 5876. What is their sum ? 49. A and B, 450 miles apart, travel towards each other. A travels at the rate of 30 miles a day and B of 35 miles a day. If B rests the second day, how far apart are they at the end of the fourth day? 50. A man bought 163 barrels of flour at $9 a barrel; 15 barrels were spoiled, and the remainder he sold at $11 a barrel. Did he gain or lose, and how much ? 51. At an election the sum of the votes received by two opposing candidates was 4324; the successful candidate received 218 more votes than his opponent. How many votes did each receive ? 52. On commencing business a merchant had $ 7852 in cash, $ 7919 in real estate, goods valued at $ 9728, a lot of lumber valued at $6930, a ship valued at $ 16834; during the first year he was in trade he gained above all his expenses $ 3195. What was he worth at the end of the year ? 53. The Gulf Stream carries 2787840000000 cubic feet of water past a given point every hour, which is 1200 times as much as the hourly discharge of the Mississippi. What is the hourly discharge of the Mississippi ? 54. There were 1032467 cigars made in Westfield in 1 month. If these were bought for 5 cents apiece, how many families would the money thus spent supply with bread for a year (365 days) if each family should consume two 8-cent loaves a day? 55. The distance from Boston to Albany is 202 miles, from Albany to Buffalo, 298 miles. How long will it take a train to pass over the road at the rate of 28 miles an hour, allowing 2 hours for detentions between Boston and Albany, 1 hour at Albany, and 3 between Albany and Buffalo ? 56. If it takes 5 yards of cloth to make a pair of shirts, what will 24 pairs cost at 15 cents per yard for the cloth, 45 cents apiece for bosoms, wristbands, and buttons, and 95 cents apiece for making ? 57. In how manv days, of 6 hours each, can the president of a bank sign 90000 bank-notes, if he signs 5 in a minute ? 58. If 8 presses can coin 19200 pieces of money in an hour, how many pieces can one press coin in a minute, 60 minutes making an hour ? Papyrus is said to have been used to write upon 2000 years before Christ, and parchment to have been invented 1810 years later; from the invention of parchment to that of paper in China was 20 years ; to printing by movable types was 1608 years more; stereotyping was invented 273 years still later. 59. How many years from the first use of papyrus, as given above, to stereotyping ? 60. In what year before Christ was paper invented in China ? 61. In what year after Christ was printing invented ? 62. There are in a certain school 47 pupils 14 years old ; 96 pupils 12 years old; 114, 11 years; 149, 10 years; and 168, 9 years old. What is their average age ? 63. If the earth is 92000000 of miles from the sun, and the moon at its full is 224000 miles farther on, and light travels at the rate of 185172 miles a second, how many seconds is it in passing from the sun to the moon and back to the earth ? 118. Questions for Review. What is ADDITION ? What is the amount ? Add orally 64 and 87. How do you write numbers to be added ? Is this absolutely necessary ? Add five numbers expressed by four figures each, and explain. Give the rule; the proof. Illustrate adding at once numbers expressed in two or more columns. What is SUBTRACTION ? What is the minuend ? the subtrahend ? the remainder ? Take orally 28 from 91. Find the difference between 368 and 7006, and explain. Give the rule; the proof. When the ininuend and difference are given, how can you find the subtrahend? When the subtrahend and difference are given, how can you find the minuend ? What is MULTIPLICATION ? What is the multiplicand ? the multiplier? the product? What are factors ? Multiply orally 45 by 6. Perform and explain an example in which the multiplier has at least two terms. Give the rule; the proof. How do you multiply by 10, 100, 1000, etc. ? How do you proceed if there are zeros at the right of the expression of the multiplicand or the multiplier, or both ? Tens x units = what ? Units x tens? Thousands x tens ? Tens x hundreds ? Ten-thousands x hundreds ? What is DIVISION? What is the dividend ? the divisor? the quotient? the remainder ? Perform and explain an example in short division ; prove the work. Perform and explain an example in long division. Give the rule ; the proof. How do you divide by 10, 100, 1000, etc. ? How do you divide when the expression of the divisor contains zeros at the right? When the dividend and quotient are given, how can you find the divisor? When the divisor and quotient are given, how can you find the dividend ? When the multiplier and product are given, how can you find the multiplicand ? When the multiplicand and product are given, how can you find the multiplier ? |