25. Allowing 2 curtains for each window and 78 inches of material for each curtain, how many yards of curtain material will be needed for the cottage? 26. How much will the curtain material cost at 49 cents a yard? 27. How much will it cost for window shades for the cottage at $1.15 each? Exercise 19. Review 1. What is the cost of laying a cement walk 50 feet long and 3 feet wide at $.20 per square foot? 2. A brick wall 40' x 1' X 8' contains how many bricks, allowing 22 bricks per cubic foot? 3. A concrete foundation 3 feet wide and 8 feet deep was placed under a building with outside measurements of 120' by 100'. How many cubic yards of concrete were used? Suggestion: Do not count the corners twice. Show that there are 2 walls 120 feet long and that the two ends between them must be considered 94 feet long on account of the side walls being 3 feet thick. 4. Each side of the roof of a tool shed is 8' by 18'. How many shingles should be ordered for laying the shingles with a 4-inch exposure to the weather? (See the suggestion following problem 19 on page 264.) 5. A hen house is 24 feet long and 10 feet wide. How many "squares" of tarred paper must be ordered to cover it? 6. The basement of a house is to be 28 feet by 36 feet. How many loads of earth must be removed to excavate it to a depth of 4 feet? 7. How many loads of earth must be removed for an excavation 28 feet long, 24 feet wide and 5 feet deep? CHAPTER IV PERCENTAGE The term per cent is widely used in business. It is a short form by which we can express the rate of gain in business investments, interest on money, discounts on bills of goods, the proportion of butter fat in milk, the rate of insuring our property against loss by fire, and the rate of commission received for selling goods. The expression per cent means hundredths. When one borrows money and agrees to pay 6 per cent of the amount each year for the use of the money, it means that he must pay 6 hundredths (or 6) of that amount for the use of the money. When we say that 4 per cent of milk is butter fat, we mean that of the milk is butter fat. In other words, in every 100 pounds of such milk, there are 4 pounds of butter fat. Instead of saying that a man gains one-tenth on the money he has invested, we say that he gains ten per cent on his money, meaning that he gains ten dollars on every hundred dollars that he has invested. Outside the business world, percentage is much employed in scientific and statistical reports. Instead of writing the words per cent, we may save time by using the sign %. Exercise 1 1. In the diagram at the right how many small squares are there in the large square? How many small squares are shaded? 2. The shaded portion represents how many hundredths of the large square? 5 Since per cent means hundredths, 100 of the large square may be expressed as 5% of the large square. The shaded portion then, is what per cent of the large square? 3. Draw a diagram on squared paper to show 2% of a large square; 8% of such a square, and 10% of a square. 4. Draw diagrams on squared paper to show the meanings of 20%; of 25%; of 50%; of 75%. 5. What is 5% of 200? The number 200 may be represented by 200 small squares in the shape of a rectangle. The heavy line in the middle divides the rectangle into two parts, each containing 100 squares. 5% of 100 of these squares has aready been shown to be 5 squares. The shaded portion of the rectangle represents 5% of 200 squares, or 10 squares. 6. Draw a diagram on squared paper to show 8% of 200 7. Draw diagrams on squared paper to represent 6% of 400; 3% of 300; 25% of 200. Exercise 2. Per Cents Expressed as Decimals 5 5% has the same value as the common fraction 150. But the common fraction may also be expressed as a decimal, .05. Then 5%=150=.05. Express the following per cents as common fractions, then as decimals as shown in the preceding form: 17. What is 6% of $300? 6% of $3001.06 of $300=? 18. What is 12% of $40? 12%.12 or .125. Find the following: 19. 4% of $150. 20. 10% of 75 pounds. 21. 1% of 200 bushels. 22. 50% of $18. 23. 20% of $400. 24. 163% of $48. 121% of $40=.125 of $40=? 25. 8% of 2000 pounds. 26. 6% of $500. 27. 37% of 40 pounds. 28. 75% of 1200 bushels. 29. 11% of $3750. 30. 3% of $126.50. 31. 2% of $26.40. 32. 40% of 800 bushels. 1One Per Cent Method: Teachers who prefer the one per cent method may substitute the following explanation: 1% of $300=100 of $300 =$3.00. 6%=6×$3.00=$18.00. Exercise 3 1. Out of every ream of 500 sheets, 4% is allowed for waste in printing. How many sheets are allowed for waste in each ream? How 2. The attendance at a basket ball game was 215. The high-school students composed 60% of the audience. many high-school students attended the game? 3. A sixth grade cleared $45.20 on a school entertainment. They spent 75% of this amount for pictures for their school room. How much did the pictures cost? 4. A stenographer saves 10% of her salary of $24 per week. How much does she save each week? At that rate how much can she save in 50 weeks? 5. Of the books in a city library, 60% are story books. How many story books are there in this library of 8500 volumes? 6. The historical section of that library forms 10% of the total number of books. How many historical books are there in the library? 7. A store handling athletic goods sells footballs costing $5.00 at a profit of 40%. How much do they make on 4 such sales? 8. In a certain sixth-grade class of 35 pupils, 60% are girls. How many girls are there in the class? How many boys? 9. In a country school, 20% of the pupils are in the first. grade. If the enrollment of the school is 25 pupils, how many pupils are there in the first grade? 10. A book that costs 40 cents is sold at a gain of 25%. What is the selling price of the book? 11. Martha raised 75 chickens. She sold 80% of them and kept the rest of them. How many did she sell? How many did she have left? |