In solving problems, the pupil will be aided by expressing the required operations using the proper symbols, as shown in the following examples. 12. How many square yards are there in a roadway 200 feet long and 40 feet wide? 200 × 40 = Ans. 13. From the freezing to the boiling point in the Centigrade thermometer is 100°; in Fahrenheit's it is 180°. How many degrees of Fahrenheit's equal 40 of 180 × 40 Centigrade? 100 14. How many degrees Centigrade equal 100 × 36 36° Fahrenheit? = Ans. = Ans. 180 15. When 360 hours of the month of July have passed, how many days remain? 16. A and B, two candidates for office, received a total of 2584 votes, A receiving 430 less than B. How many votes did each receive? 2584430 = A's. A's 430 B's. 17. If 19,200 coins can be stamped by 8 presses in 1 hour, how many can be stamped by 1 press in 40 minutes? 19200 × 40 8 × 60 = Ans. 18. For how much must 8 tons of hay, which cost $17.50 a tou, sell, to gain $3.75 per ton? ($17.50 + $3.75) × 8 = Ans. 19. $2500 was paid for 10 acres of land. For how much must it be sold to gain $ 200 per acre? $2500 + $200 x 10 = Ans. 20. A merchant sold 40 yards of cloth for $140, having bought it for $2.50 a yard. What was his gain per yard? $2.50 Ans. $140 = Ans. 21. The charges of a student in a preparatory school last year were, for tuition, $75, and for incidental expenses $9. This year in college the charges were twice as much for tuition, and 5 times as much for incidentals. What was the total cost for the two years? $75+ $9+ $75 × 2 + $9 × 5: 22. I owe John Brent $600, due 6 months hence. If I pay him 1 half now, he is willing to take off 5 cents on a dollar of the other half of the debt. What will the balance be? $6002 $0.05 × 300 = Ans. 23. Find the cost of storage of the following lots of flour at 3 cents on a barrel per month. 200 barrels, 2 months. 150 barrels, 1 month. 175 barrels, 3 months. 280 barrels, 2 months. = [(200+280) × 2 + 150 + 175 × 3] × 3 cents Ans. Miscellaneous Oral Examples. 149. Illustrative Example. a. If 8 yards of cotton cost 72 cents, how much will 5 yards cost? SOLUTION. - If 8 yards cost 72 cents, 1 yard will cost 1 eighth of 72 cents, or 9 cents, and 5 yards will cost 5 times 9 cents, or 45 cents. Ans. 45 cents. b. If $3.50 is paid for 7 days' work, how much will be paid for 10 days' work? c. How many hours' work @ $0.12 an hour will pay for 3 loaves of bread @ $0.08 a loaf and 4 lb. of beef at $0.09 a lb. ? d. If 9 rows of corn yield 36 bushels, how many bushels will 20 similar rows yield? e. If an express train runs 114 miles in 3 hours, how far can it go in 4 hours ? f. If $2 will buy 1 bushel 2 pecks of pease, how many pecks will $12 buy? g. If 6 boys can put the schoolroom in order in 10 minutes, how many boys can do the work in 12 minutes? h. A field of rye was reaped by 12 men in 5 days. What length of time would be required for 15 men to reap the same amount? i. If a cistern can be emptied in 20 minutes by 3 pipes. of the same size, in what time can it be emptied when only 2 of the pipes are open? j. A sea breeze was felt on the coast at half-past four. If its velocity was 4 miles an hour, at what time was it felt 9 miles inland? k. The Israelites left Egypt in the year 1491 B.C. In what year did they enter Canaan 40 years later? 7. If it takes a dozen lemons to make lemonade for 24 persons, how many lemons must be allowed for 300 persons? m. When a floor is 11 feet wide, what must be its length to contain 132 square feet? NOTE. Since the number of feet in length multiplied by the number of feet in width equals the area, to find the length, 132 must be divided by the number of feet in the width (Art. 108). n. A grocer has 4 grades of coffee worth 29 cents, 21 cents, 40 cents, and 42 cents, which he mixes, using equal quantities of each. At what price can he afford to sell the mixture? o. It took 12 yards of carpeting 3 quarters of a yard wide to carpet a room. How much would it take of carpeting that is 4 quarters wide? p. A newsboy sells papers for an agent at 5 cents each, and is allowed 2 cents a copy for every paper sold. If his allowance is 24 cents, how many papers does he sell, and what does the agent receive? q. What is the profit in buying 10 shares of stock at $93 per share and selling them at $115 a share? 150. Miscellaneous Examples for Written Work. 24. If 6 yards of plush cost $13.50, what is the cost of 13 yards? 25. Five hundred passengers were carried by special train for $65.00. How much should be paid for carrying a family of 7 persons at the same rate? 26. A crew of 12 persons had provisions for 36 days, when they took in 9 more persons from a wreck. How many days' provision had they for all? 27. How many strips of flooring 4 inches wide must be used to lay a floor which requires 144 strips 6 inches wide? 28. How many loaves of bread, 7 ounces of flour to a loaf, can be made from a barrel of flour (196 pounds) ? 29. At 17 cents a yard for paper bordering, what will be the cost of bordering for a room 16 feet long and 14 feet wide? 30. What must be the length of a lot of land 80 feet wide to contain 10,000 square feet? 31. A cheese weighing 24 pounds cost $3.60. For how much a pound should it be sold to give a profit of 10 cents a pound? 32. What shall I receive for selling $7800 worth of goods if I receive $7 on each $100? 33. When taxes are $16 on $1000, how much is a person taxed who has $13,000 worth of real estate and $28,000 of personal property? 34. The bell of St. Peter's in Rome weighs 18,600 pounds; that of the Kremlin in Moscow, the largest in the world, weighs 448,000 pounds. How many times as heavy as the former is the latter? 35. 18 acres of land were bought for $4050 and sold for $5000. What was the gain per acre? 36. If the land above had been sold for $3900, what would have been the loss per acre? 37. What must be paid for insuring my house worth $2500, at $1.50 on each $100 ? 38. It is estimated that in 1890 there were 77,875,901 people in North America, 34,440,619 in South America, and 366,571,583 in Europe. How many more people were there in Europe than in North and South America together? 39. Mr. Jaynes bought 41 acres of land at $60 an acre, and sold it for $3000. Did he gain or lose, and how much? How much per acre? 40. One person can make by hand 40 pairs of sleeve buttons in a day, another with a machine can make 9000 pairs in a day. How many men working by hand would be required to do a day's work of one man with a machine? 41. Dora deposited in the savings bank $3.20 in May, twice the amount in June, $4.75 in July, $5.80 in August; she took out $8 in September, deposited $18.48 in October, $4.78 in November, and took out $15.50 in December. How much remained in the bank? 42. What is your ice bill for the year if you commence to take ice in May and pay $9 from May through September, and 30 cents a hundred for the remainder of the year, using 260 pounds in October, 155 in November, and 85 in December? 43. A dealer sells a bushel of berries in quart boxes for which he receives $0.15 a box. If he pays $3 for his berries and 2 cents for every box he uses, what are his profits? 44. Four children amused themselves by counting watermelon seeds on their plates. They counted 25, 70, 143, and 212. Suppose these were 1 third of the seeds in the whole melon, how many seeds did the melon contain? 45. In 1880 Boston had 362,839 inhabitants; in 1890 there were 448,477 inhabitants. What was the increase in 10 years, and the average increase per year? |