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1.5 Story Problems Name ___________________________ Learning Objective: A.SSE.2 I will rewrite an expression using distribution A.SSE.2 I will rewrite an expression by combining like terms A.REI.3 I will solve a linear equation that involves combining like terms A.REI.3 I will solve a linear equation that involves distribution A.REI.1 I will explain each step in solving an equation with combining like terms A.REI.1 I will explain each step in solving an equation with distribution Solve each problem below by writing an equation and showing all work. 1. Jon has a board that is 60 inches long. He plans to use it to make 4 shelves whose lengths are to be a series of consecutive even integers. How long should be each shelf? Answers: _____, _____, ____, ____ 2. The length and width of a rectangle are consecutive even integers. If the perimeter is 52 feet, what is the length and the width of the rectangle. Answers: _____, _____ Set up each problem by writing an equation. DO NOT SOLVE. 3. Fifty four automobiles in a parking lot are divided into two groups. One group has twice as many automobiles as the other. 4. Tom and Alfredo scored a total of 25 points playing basketball. Alfredo scored 4 times as many points as Tom. 5. Alice’s age is 2 years more than 3 times Beulah’s age. The sum of their ages is 58 years. 6. Bob caught 3 times as many fish as Marilyn. Together they caught 24 fish. 7. Arnold’s golf score was 12 strokes less than Jack’s. The sum of their scores was 150. 8. Nelda’s lunch cost $1.50 less than Wong’s lunch. Together the bill was $8. 9. A restaurant bill was $47.50. Irene’s share was $8 less than twice Charlie’s share. Using one variable, write an equation for each problem. DO NOT SOLVE. (draw a picture) 10. The width is half the length and the perimeter is 20 cm. 11. The length is 4 more than the width and the perimeter is 32 m. 12. The perimeter of a rectangle is 52 inches. The width is 10 inches less than the length. 13. The length of a rectangle is twice the width. The perimeter is 18 in. 14. The width of a rectangle is 5 cm less than twice the length. The perimeter is 38 cm. 15. Two angles are complementary. The larger angle is 4 times greater than the smaller angle. 16. Two angles are complementary. The measure of the angles are in a ratio of 5:1. 17. Two angles are supplementary. The larger angle is 5 times greater than the smaller angle. 18. The measure of the supplement of an angle is 8 more than three times the original angle. Answers: 1) 12 in, 14 in, 16 in, 18 in 9) x + 2x – 8 = 47.50 3) x + 2x = 54 11) 4x + 8 = 32 5) b + 3b + 2 = 58 13) 6x = 18 7) j + j – 12 = 150 15) x + 4x = 90 17) x + 5x = 180