THE LITERAL EXPRESSION A. Write an expression for the cost of 5 apples if one apple costs 6 cents; if one apple costs c cents. If one apple costs 6 cents, 5 apples cost 5 × 6 cents. B. If x is a given number, write an expression for a number 5 larger than x. If x = the given number, then x+5= the number 5 larger than x. PROBLEMS 1. If one book costs d dollars, how much will six books of the same kind cost? 2. A boy walks at the rate of m miles an hour. How far will he walk in 3 hours? 3. A man earns $30 a week. How much will he earn in 2 weeks? in x weeks? 4. If a number is represented by n, how large is twice the number? three times the number? five times the number? 5. A man earns d dollars a week. How much does he earn in a year? 6. If n represents a number, what represents one half of the number? two thirds of the number? 7. There are x boys in Miss Johnson's room, and 5 more girls than boys. How many girls are there? 8. The difference between two numbers is 10. If x represents the smaller number, what represents the larger number? B. The sum of two numbers is 20 and the larger number is three times the smaller. Find the numbers. Let x = the smaller number. Then 3x the larger number. = But the sum of the two numbers equals 20. In each of these problems represent the unknown quantity by some letter and form an equation. Check all these problems by showing that the results satisfy the statements of the problems. 1. What number multiplied by 13 equals 78? 2. What number multiplied by 17 equals 136? 3. If of a number equals 16, find the number. 4. If 1 times a number equals 25, find the number. 5. If 7 is added to 5 times a number, the result is 52. Find the number. 6. If 5 is subtracted from four times a number, the result is 27. Find the number. 7. If 3 is taken from six times a number, the result is 45. Find the number. What must 8. The base of a parallelogram is 16 ft. the altitude be to give an area of 192 sq. ft.? (Let h tude.) = alti 9. What must the altitude of a triangle be if the base is 18 in. and the area is 54 sq. in.? 10. What is the base of a triangle with an altitude of 8 ft. if the area is 48 sq. ft.? 11. Eighty-two is 66% of what number? 12. Forty-five is 60% of what number? 13. Fifty-four is what per cent of 72? 14. Forty-two is what per cent of 120? 15. The sum of two numbers is 42 and the larger is five times the smaller. Find the numbers. 16. Separate 75 into two parts of which one is four times the other. 17. Divide $84 between A and B so that A shall receive six times as much as B. 18. Mrs. Horton bought a certain number of yards of silk and three times as many yards of linen. She bought 36 yd. in all. How many yards of each did she buy? 19. A and B own 420 acres of farm land, A owning twice as much land as B. How large is each farm? 20. The length of a lot is three times the width. The distance around the lot is 128 yd. Find the dimensions of the lot. (Let w = width.) 21. I have 48 ft. of wire fencing with which to inclose a rectangular garden. What will be the dimensions of the garden if the length is to be twice the width ? CHAPTER XII INDIRECT MEASUREMENT; ANGLES; SQUARE ROOT Often it is possible to obtain lengths and distances, which cannot easily be obtained by direct measurement, by making use of other known distances. This principle is used so frequently in everyday life that a few applications are given in this chapter. RATIO The ratio of two quantities is the quotient obtained by dividing one of the quantities by the other. The two quantities must be expressed in terms of the same unit. The fraction is reduced to its lowest terms. The ratio of 3 to 5 is equal to . The ratio of 18 in. to 2 ft. (or 24 in.) is 1, or 2. This is simply another way of saying that 18 in. is of 2 ft. The ratio of 2 lb. (or 32 oz.) to That is, 2 lb. is of 12 oz., or 2 Find the ratio of 1. 5 to 15. 2. 12 to 14. 3. 15 to 20. 12 oz. is 12 or §. 6. 20 to 15. 7. 18 yd. to 30 yd. 8. 25 rd. to 20 rd. 1. A city lot is 60 ft. by 150 ft. Find the ratio of the width to the length. 2. A bicycle that cost $24 was sold for $30. Find the ratio of the cost to the selling price. 3. Margaret is 4 ft. tall and Betty is 5 ft. 4 in. Find the ratio of their heights. 4. There are 200 boys and 240 girls in the Emerson School. Find the ratio of the number of boys to the number of girls. 5. Joseph is twelve years old and his father is thirty-six. Joseph's age is what part of his father's age? 6. Florence bought a 2-lb. cake of chocolate and used 4 oz. in making fudge. What part of the whole cake was left? 7. Two boys walked 14 miles on Saturday. They walked 8 miles before stopping for lunch. What part of the 14 miles was walked in the afternoon? 8. Alfred spelled correctly 22 words in a test of 50 words. What is the ratio between his correct words and the entire test? SIMILAR FIGURES Figures that have the same shape are similar figures. They may or may not be of the same size. The triangles ABC and DEF are similar. In similar triangles the corresponding B C E D angles are equal and the corresponding sides have the same ratio. In the given triangles, angle A = angle D, angle B = and if AB, BC, etc., represent the lengths of the sides expressed in the same units, |