35. If I buy 8 boxes of starch, each box containing 24 pounds, at 8 cents a pound, and offer in payment a $20 bill, what change shall I receive? 36. Elsie and Lottie have together $5.70, and Lottie has 40 cents more than Elsie. How much money has each? 37. If 14 men can do a piece of work in 56 days, how long will it take 28 men to do half the work? 38. I bought two horses. The first cost $312, and the second $40 less than the first. How much did the two horses cost? 39. If 19 tons of coal run an engine 703 miles, how far will 17 tons run it? 40. A farmer exchanged 4 cows, worth $79 each, for a span of horses. What were the horses worth apiece? 41. A horse cost $235, a carriage $219, and a hack 3 times as much as both. What did all three cost? 42. A merchant bought 42 bales of cloth, each bale containing 36 pieces, and each piece 38 yards, at 9 cents a yard. He sold the whole at 11 cents a yard. How much did he gain? 43. If I take 764 bushels from 2000 bushels twice, how much will remain ? 44. A drover with $2144 bought as many horses as possible for $165 each, and spent the remainder for sheep at $4 a head. How many of each did he buy? 45. How many times 945 will make 23,625? 46. Twenty men built a school-house in 56 days. In how many days could 70 men have built it? 47. 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? 48. A school uses 36 crayons a day. Since a gross is 12 dozen, how many gross will it use in 40 weeks, provided there is no school on Saturday? 49. 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 75 cents apiece for making? 50. A clerk has a salary of $42 a month, and his expenses are $27 a month. How many years will it take him to lay up $900 ? 51. Find the cost of 267 yards of cotton at 13 cents a yard, and twice as much at 12 cents a yard. 52. There are in a certain school 37 pupils 14 years old; 76 pupils 12 years old; 114, 11 years old; 149, 10 years old; and 168, 9 years old. What is their average age? 53. A man paid $375 for a piano, $13 for freight and cartage, and $2 for tuning it. He then rented it for 7 quarters at $15 a quarter, and afterwards sold it for $325. Did he gain or lose, and how much? 54. Two men leave the same place and travel in opposite directions, one at the rate of 30 miles a day, and the other at the rate of 37 miles per day. How far will they be apart at the end of 14 days? 55. If the men traveled in the same direction, how far apart would they be in the same time ? 56. A, B, and C have together $198. A and C have $145. A and B have $99. How much has each ? 57. Howard, Roy, and Jamie went fishing, and together caught 77 fish. Of these, Howard and Jamie together caught 58. Howard's and Roy's, when put together, numbered 54. How many did each catch? 58. A farmer sold 18 calves at the rate of 3 for $33 How much did he get for them? 59. If 117 tons of coal are worth $702, how much are 235 tons worth? 60. If 12 barrels of flour are worth $132, what will 36 barrels cost? 61. If a farmer receives $2275 for '13 horses, for how much would 27 horses sell at the same rate? 62. A's farm contains 227 acres; B's lacks 12 acres of being twice as much; C's lacks 42 acres of being 3 times as much as B's; and D's contains as much as A's and C's. How many acres are there in each farm? 63. A farmer wished to obtain $260. He sold 72 bushels of wheat at $1.50 per bushel, and enough apples at $2 per barrel to obtain the sum required. How many barrels of apples did he sell? 64. If a bookkeeper receives $1400 per year for his services, and his expenses are $840, in what time can he save enough to buy 32 acres of land at $140 per acre? 65. A man starting out on a journey took $200. He paid for railroad fare $67; for berth in sleeping car, 4 days, $2 a day; for hotel bills, 15 days, $3 a day; and for other expenses, $25. How much money had he left? 66. The greater of two numbers is 4056, and their differ ence is 3650. What is the less number? 67. The divisor is 534, and the quotient 43. What is the dividend? 68. The subtrahend is 34,203, and the remainder is 8706 What is the minuend? 115. The parenthesis, (), shows that the numbers included within it are to be subjected to the same operation. Thus, (153) × 3 means that 153, or 12, is to be multiplied by 3; but 15 3 x 3 means that 15 is to be diminished by 3 × 3, or 9. (7+2) × 5 means that the sum of 7 and 2 is to be multiplied by 5; but 7 + 2 × 5 means that 7 is to be increased by 2 × 5. (75) 6, or divided by 6. [(9 + 3) × 2 7 +5, means that the sum of 7 and 5 is to be 6 3] 7 means that the sum of 9 and 3 is to be multiplied by 2, the product diminished by 3, and the remainder divided by 7. (7 × 8)–(5 × 5) means that the product of 7 and 8 is to be diminished by the product of 5 and 5. 116. The Vinculum, instead of the parenthesis. Thus, 5 3 x 3 or [5-3]×3 may be used instead of (5 3) x 3. 117. In finding the value of expressions in which the parenthesis, vinculum, or brackets are used, First, perform the operations on the numbers that are written within parenthesis and brackets, or under the vinculum, as indicated by the signs. Next, multiply and divide, as indicated by the signs and. Finally, add and subtract, as indicated by the signs + and 5. 4+16÷ 4. 6. (4+16) 4. (3 × 4) – (2 × 3). 3 12. [(5+6) × 4-5 × 8] × 9. 13. (3 × 4) x 5-(9+7)÷8. 7. (3+4) x (8-5). 14. 2+12÷4+(8+8÷4)÷2, 15. 312+36)— (381 — 215) — 65. 16. (214-81)-(115-18+6)+10. 17. (413-200)-(118-24 - 4 + 6) + 3. 20. (5+2+6) × 4-(7+8-3)+6+10. 22. (993)÷8 − (86 +10) ÷ 12 + (3 + 6) ÷ 3. FACTORING. 118. 1. What is the product when 3 and 2 are multiplied together? What are 3 and 2 of their product? (Art. 86.) 2. What factors will produce 9? 3. What numbers when multiplied together will produce 12? What are 3 and 4, or 6 and 2 of their product? 4. What are the factors of 20? 5. What are the factors of 27 ? Of 36? Of 15? Of 25? Of 32 ? Of 33? Of 50? What else may 7 be 6. What are the factors of 21 ? 7. What are the factors of 63? called of 63 besides a factor? 8. If 9 is one of two factors of 18, what is the other factor? If 3 is one of the factors? If 6 is one of the factors? 9. What numbers will exactly divide 18? 25? 36? 10. Give the exact divisors of 42; 96; 35; 50; 27; 72. 11. Give the factors of 36; 40; 48; 70; 80. 12. Give the exact divisors of 44; 56; 64; 84; 96. 13. Name the exact divisors of 49; 88; 63; 24; 27. 14. What numbers between 0 and 10 cannot be exactly divided by any number except themselves and 1? numbers between 10 and 20? Between 20 and 30? What 15. What numbers between 0 and 10 can be exactly divided by other numbers besides themselves and 1? Between 10 and 20? Between 20 and 30? 16. Select from the following the numbers that have no exact divisors except themselves and 1: 35, 42, 63, 56, 61, 47, 49, 81, 37, 26, 18, 45. |
