35. Find the cost of a stone wall 30 ft. long, 24 ft. thick, and 6 ft. high, at $5.30 a perch. 36. How much will it cost to cement the floor of a cellar, 40 ft. by 20 ft., at 90¢ a square yard ? 37. A street 50 ft. from curb to curb is opened for a distance of 300 yards. How much will it cost to excavate it to a depth of 1 foot at 40$ per cubic yard ? 38. How much will the curb of this street cost at 26 ¢ per linear foot ? 39. The sidewalk on this street is 12 ft. wide, including a curb of 8 inches. How much will the brick for the walk cost, at $9 per thousand, if the exposed surface of a brick is 4 in. x 8 in. ? . 40. A farmer built a circular silo 12 ft. in diameter and 24 feet high. Find its contents in cubic feet. 41. How many blocks of ice, 2 ft. x 1 ft. x 1 ft., can be packed in a car 6 ft. x 8 ft. x 40 ft. ? Ice is .92 as heavy as water. Find the weight of the ice if a cubic foot of water weighs 621 lb. 42. A cistern is 4 ft. in diameter and 6 ft. deep. How many barrels of water will it contain ? 43. Estimate the weight of the water in a tank 8 ft. long, 6 ft. wide, and 2 ft. deep. 44. A vault is 5 ft. square and 6 ft. deep. How much will it cost to cement the sides and bottom at $.50 per sq. ft. ? 45. A circular amusement park is 80 rods in diameter. Find the cost of the boards for a tight board fence 8 ft. high, inclosing the park, at $ 20 per M. 46. A corner lot in Seattle is 25 ft. by 100 ft. At $25 per M., what will be the cost for 2-inch plank for a 10-foot sidewalk in front and on the side, including the corner ? NOTE. — Illustrate by diagram. 47. Mr. Ames owns a 50-ft. lot fronting on a street 60 ft. wide from curb to curb. The law compels him to pay of the cost of paving the street in front of his lot. How much will it cost at $2.90 per square yard ? 48. A tank open at the top is 50 ft. long, 4 ft. wide, and 3 ft. deep. How much will the lead for lining it cost, at 8$ per pound, estimating 4 pounds to a square foot ? 49. Clay weighs 1.2 as much as the same volume of water. Estimate the weight of a load of clay. 50. Find the cost of painting the sides and ends of this hay barn at 15$ per square yard, å EYE and the cost of stain ing the roof at 124 per 40 square yard. 51. In excavating for a cellar 60 ft. long, 30 ft. wide, and 8 ft. deep, the material was evenly distributed over a lot 90 ft. by 40 ft. To what depth was the lot covered ? 52. A two-story school building has 8 rooms 30 ft. x 32 ft. and a hallway 28 ft. x 15 ft., on each floor. How much will the flooring for the building cost at $44 per M. ? 53. In digging a sewer 31 feet in width and 8 feet deep, 12444 cubic yards of earth were excavated. Find the length of the sewer in feet. 54. A frame building is 42 ft. long, 28 ft. wide, and 22 ft. to the square, or part below the gable. The altitude of the gable is 10 ft. Allowing $10 for painting the cornice, estimate the total cost of painting the building with 3 coats, at 30$ per square yard, no allowance being made for the openings. (Draw the figure to show the gables.) ANALYSIS THE EQUATION 1. 8= 8 3. 8= 12 – 4 In example (1) we have an equal number on each side of the equality sign. In example (2) we have 8+4=12 ; but in example (3), in order to preserve the equality, when we take 4 from the left of the equality sign in example (2), we must sub- Test: 8 + 4 = 12 tract 4 from the number on the right - 4 - 4 of the equality sign. Thus 8= 12 – 4. 8 = 12 – 4 4. 8= 6 + 2 5. 8– 2 = 6 Observe that a number may be moved from one side of an equation to another by changing its sign. . Written Work Change the following so that the first number in each problem will stand alone at the left of the equality sign: 6. 20 – 10 = 10 10. 75 – 20 = 55 14. First add, then subtract, 5 from each member of the equation 10 = 10. (a.) 10 = 10 (6.) 10 = 10 +5 = +5 15 = 15 The same number may be added to or subtracted from both sides of an equation without destroying the equality. Factors and their Product 1. 5 times a certain number is 35. What is the number? FACTORS PRODUCT 5 x the number = 35 The number = 35 + 5 = 7 When the product of two factors is divided by one of the factors, the quotient is the other factor. When one of the factors is unknown, it may be found by dividing the product by the known factor. State the factors and solve: 2. 5 times John's money = $40. How many dollars has he ? 3. 2 times A's sheep are 60. How many sheep has he? 4. 6 times B's age is 360 years. How old is he? . 5. of a number is 150. What is the number? 6. 1.25 times a number is 30. What is the number? 7. .75 of a number is 75. Find the number. 8. of a number is 75. Find the number. 1 of the number = 75 The number = 3 x 75 = 225 The work may be shortened by calling the unknown factor x. For example, 9. Mr. Brown's profits equal 4 times Mr. Long's profits, and together their profits are $125. Find the profits of each. Let x= Mr. Long's profits. 4 x = Mr. Brown's profits x = $25, Mr. Long's profits. 4 x = $100, Mr. Brown's profits. 10. Mr. Byers and Mr. Boydson together have 240 acres of land, and Mr. Byers has 40 acres more than Mr. Boydson. How many acres has each? Let x = the number of acres in Mr. Boydson's farm. x + 40 = the number of acres in Mr. Byers's farm. 2 x = 240-40 x = 100, the number of acres in Mr. Boydson's farm. * + 40 = 140, the number of acres in Mr. Byers's farm. Solve first by written analysis, then orally : 11. Four times my money and $6 more is $50. How much money have I ? 12. $80 is $5 more than twice the cost of a bicycle. Find the cost. 13. Harry's age plus 1 his age plus 6 years equals 30 years. How old is he? 14. 21 times the number of books in Henry's library, less 5, equals 70. How many books has he? 15. James spent 1 of his money for a top, of it for a ball, and had 10 cents remaining. How much money had he at first ? 16. After paying 1 and 1 of my debts, I still owed $25. How much did I owe at first ? 17. A merchant lost of his capital, then gained as much as he had left, and then had $10800. How much was his capital at first ? 18. Robert's money, diminished by 1 and of itself, equals $1.25. How much money has he? 19. After a fruit dealer had sold of his apples, and 1 of the remainder, he had 12 bushels left. How many bushels had he at first ? 20. If of Wilbur's money is increased by 4 of of his money, the sum will be $54. How much money has he ? |