194 CHAPTER 1 Equations and Inequalities 7. Concept Check If x represents the number of pennies in a jar in an applied problem, which of the following equations cannot be a correct equation for finding x? (Hint: Solve the equations and consider the solutions.) A. 5x + 3 = 11 B. 12x + 6 = -4 C. 100x = 501x + 32 D. 61x + 42 = x + 24 8. Airline Carry-On Baggage Size Carry-on rules for domestic economy-class travel differ from one airline to another, as shown in the table. Airline Size (linear inches) Alaska 45 Delta 45 Southwest 50 Spirit 50 Sun Country 51 United 45 Data from travel-made-simple.com To determine the number of linear inches for a carry-on, add the length, width, and height of the bag. (a) One Samsonite rolling bag measures 8 in. by 15 in. by 21 in. Are there any airlines that would not allow it as a carry-on? (b) A Lark wheeled bag measures 10 in. by 14 in. by 22 in. On which airlines does it qualify as a carry-on? Solve each problem. 9. Dimensions of a Square If the length of each side of a square is decreased by 4 in., the perimeter of the new square is 10 in. more than half the perimeter of the original square. What are the dimensions of the original square? 10. Distance from a Library Jayde can ride her bike to the university library in 20 min. The trip home, which is all uphill, takes her 30 min. If her rate is 8 mph faster on her trip there than her trip home, how far does she live from the library? 11. Alcohol Mixture Barak wishes to strengthen a mixture that is 10% alcohol to one that is 30% alcohol. How much pure alcohol should he add to 12 L of the 10% mixture? 12. Loan Interest Rates A realtor borrowed $90,000 to develop some property. He was able to borrow part of the money at 5.5% interest and the rest at 6%. The annual interest on the two loans amounts to $5125. How much was borrowed at each rate? 13. Speed of a Plane Mary Lynn left by plane to visit her mother in Louisiana, 420 km away. Fifteen minutes later, her mother left to meet her at the airport. She drove the 20 km to the airport at 40 km per hr, arriving just as the plane taxied in. What was the speed of the plane? 14. Toxic Waste Two chemical plants are releasing toxic waste into a holding tank. Plant I releases waste twice as fast as Plant II. Together they fill the tank in 3 hr. How long would it take the slower plant to fill the tank working alone? 15. (Modeling) Lead Intake As directed by the “Safe Drinking Water Act” of December 1974, the EPA proposed a maximum lead level in public drinking water of 0.05 mg per liter. This standard assumed an individual consumption of two liters of water per day. (a) If EPA guidelines are followed, write an equation that models the maximum amount of lead A ingested in x years. Assume that there are 365.25 days in a year. (b) If the average life expectancy is 72 yr, find the EPA maximum lead intake from water over a lifetime.
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