118 CHAPTER 1 Equations and Inequalities 1.2 Exercises CONCEPT PREVIEW Solve each problem. 1. Time Traveled How long will it take a car to travel 400 mi at an average rate of 50 mph? 2. Distance Traveled If a train travels at 80 mph for 15 min, what is the distance traveled? 3. Investing If a person invests $500 at 2% simple interest for 4 yr, how much interest is earned? 4. Value of Coins If a jar of coins contains 40 half-dollars and 200 quarters, what is the monetary value of the coins? 5. Acid Mixture If 120 L of an acid solution is 75% acid, how much pure acid is there in the mixture? 6. Sale Price Suppose that a computer that originally sold for x dollars has been discounted 60%. Which one of the following expressions does not represent its sale price? A. x - 0.60x B. 0.40x C. 4 10 x D. x - 0.60 7. Acid Mixture Suppose two acid solutions are mixed. One is 26% acid and the other is 34% acid. Which one of the following concentrations cannot possibly be the concentration of the mixture? A. 24% B. 30% C. 31% D. 33% 8. Unknown Numbers Consider the following problem. The difference between seven times a number and 9 is equal to five times the sum of the number and 2. Find the number. If x represents the number, which equation is correct for solving this problem? A. 7x - 9 = 51x + 22 B. 9 - 7x = 51x + 22 C. 7x - 9 = 5x + 2 D. 9 - 7x = 5x + 2 9. Unknown Numbers Consider the following problem. One number is 3 less than six times a second number. Their sum is 46. Find the numbers. If x represents the second number, which equation is correct for solving this problem? A. 46 - 1x + 32 = 6x B. 13 - 6x2 + x = 46 C. 46 - 13 - 6x2 = x D. 16x - 32 + x = 46 10. Dimensions of a Rectangle Which one or more of the following cannot be a correct equation to solve a geometry problem, if x represents the length of a rectangle? (Hint: Solve each equation and consider the solution.) A. 2x + 21x - 12 = 14 B. -2x + 715 - x2 = 52 C. 51x + 22 + 5x = 10 D. 2x + 21x - 32 = 22 Solve each problem. See Example 1. 11. Perimeter of a Rectangle The perimeter of a rectangle is 294 cm. The width is 57 cm. Find the length. 12. Perimeter of a Storage Shed Michael must build a rectangular storage shed. He wants the length to be 6 ft greater than the width, and the perimeter will be 44 ft. Find the length and the width of the shed. Note: Geometry formulas can be found on the back inside cover of this text.
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