times 800 lb. If 800 dollars. lb. of hay is worth $3.00, 1 ton is worth (a) If 800 lb. of flour is worth $18.50, how much is 1 ton worth at the same rate? 2. One mile is times 80 rd. If it costs $30 to build 80 rd. of fence, to build one mile of similar fence will cost dollars. (b) If it costs $375 to make 80 rd. of road, how much will it cost to make 1 mile of road at the same rate? 3. One hour is and times 24 minutes. Harry rode 5 miles in 24 minutes; this was at the rate of an hour. (c) A locomotive moved 19 miles in 24 minutes. This was equal to what rate per hour? pump rod 4. One minute is times 20 seconds. A made 18 strokes in 20 seconds; this was at the rate of strokes a minute. (d) A certain pulley revolves 106 times in 20 seconds. What is its rate of revolution per minute? (e) How many times does it revolve in one hour? (f) Find how many times your pulse beats in 20 seconds. This is at what rate per minute? Per hour? If 12 oz. cheese is worth 154, 1 lb. is worth times 12 ounces. (g) If 12 ounces of onion seed is worth 724, how much is 1 pound worth? 6. If 50 sq. rods of land is worth $20, at the same rate 1 acre is worth dollars. (h) If 50 square rods of land is worth $345, how much is 1 acre worth at the same rate? (g) $747 is 121 49 is 12% less than 54 is 10% less than 28 is 30% less than per cent more than how many dollars? (h) $868 is 12 per cent less than how many dollars? (i) $572 is 10 per cent more than how many dollars? (j) $729 is 10 per cent less than how many dollars? (k) $299 is 30 per cent more than how many dollars? (1) $350 is how many per cent less than $500? * Think of x as standing for the number sought. Then 45 x and 1 eighth of x, org of x. Since 45 is 9 eighths of x, 1 eighth of x is 5, and the whole of a is 8 times 5 = 40. † 49 = x less 1 eighth of x, or of x. Since 49 is of x, 1 eighth of x is 7, and the whole of x is 8 times 7 = 56. PERCENTAGE. 1. Five years ago the population of a certain city was 6000; it has increased 33%; its present population is (a) Eight years ago the population of a certain city was 9750; it has increased 33%. What is its present population? 2. A man sold a horse for $100 which was 25% more than he gave for it. He gave dollars for the horse. (b) A man sold a farm for $6825 which was 25% more than he gave for it. How much did he give for the farm? 3. Alice has 504; than Alice; Alice has Jane has 604; Jane has % less than Jane.* -% more (c) Mr. Lyon has 600 acres of land; Mr. Whitney has 400 acres. Mr. Lyon has how many per cent more than Mr. Whitney? (d) Mr. Whitney has how many per cent less than Mr. Lyon? 4. By selling a horse for $60, the owner would lose 25%; the horse cost dollars. (e) By selling a farm for $4320, the owner would lose 25%. How much did the farm cost him? 5. By selling a horse for $60, the owner would gain 25%; the horse cost dollars. (f) By selling a farm for $5300, the owner would gain 25%. How much did the farm cost him? 6. 25% of the vinegar in a cask leaked out and 36 gal. remained; before the leakage there were gallons. (g) 25% of the water in a tank leaked out and 465 gallons remained. How many gallons in the tank before the leakage? * In one part of this problem 50 is the base; in the other part, 60 is the base. REVIEW. 1. The sum of three numbers is 27; two of the numbers are 8 and 10; the other number is (a) The sum of three numbers is 2756; two of the numbers are 784 and 975. What is the other number? 2. Arthur rode on his bicycle three consecutive hours; the first hour he rode 12 miles; the second hour, 10 miles, and the third hour 8 miles; his average speed per hour miles. was (b) The attendance at a certain school for one week was as follows: Monday, 35; Tuesday, 38; Wednesday, 37; Thursday, 36; Friday, 34. What was the average daily attendance? * 3. At $7 per ton, 2 tons of coal cost (c) At $348 an acre, how much will 5 acres cost? (d) At $348.50 an acre, how much will 6.5 acres cost? (e) Compare the answers to (c) and (d). How much is their difference? 4. The first day of January, 1897, was Friday. Tell the day of the week of the first day of January of each of the (f) Upon what day of the week will the first day of January, 1925, occur? 5. A plot of a certain garden is drawn on a scale of 20 feet to an inch. A line 33 inches long represents feet. (g) A certain map is drawn on a scale of 25 mi. to an inch. A line 151⁄2 in. long represents how many miles ? * 2 times 7 and 1 half of 71. † Remember that the year 1900 is not a leap year. MISCELLANEOUS PROBLEMS. 1. In a pane of glass 9 in. by 12 in. there are inches. sq. (a) How many square incnes in 36 panes of glass each 9 in. by 12 in.? (b) How many square feet? 2. Mr. Black received $30 per month as rent for a house. In one year he received dollars. (c) At $35 per month, how much is the rent of a house. for 2 years and 6 months? 3. I paid $2.00 for coffee at 25¢ a pound; I purchased pounds. (d) Paid $34.75 for coffee at 25¢ a pound. How many pounds were purchased? 4. In a floor 12 ft. by 12 ft. there are square feet; (e) In a lot 24 feet by 96 feet, there are how many square feet? (f) How many square yards? 5. If a train moves at the rate of 20 miles an hour, to hours. move 110 miles will require (g) If a train moves at the rate of 35 miles an hour, how long will it take to go 1000 miles? 6. A boy bought 10 chickens for 25¢ each, and 10 for 354 each; the average price paid was — cents. (h) A man bought 10 horses at $135 each and 10 at $124.50 each. What was the average price? 7. A man sold a horse at of what it cost him, thereby losing $10; the horse cost him. dollars; he sold it for dollars. (i) A man sold a farm for of what it cost him, thereby losing $1275. How much did the farm cost him? (j) For how much did he sell it? |