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College Prep Algebra Homework Name: ________________ Date: _________________ HW Lesson 3.7B: Applications of Linear Equations Write and solve a linear equation for each of the following application problems. 1. Ms. Adams has 32 ounces of water in a bottle. She can drink 5 ounces an hour. a. How much water does she have left after n hours? ______________________ b. How many hours will it take her to finish the bottle of water? ___________ 2. At a party store, helium balloons cost 79 cents each and a box of favors costs $11.95. You have $40 to spend and you need two boxes of favors. How many balloons can you buy? There is no sales tax. ___________ 3. A chemist has solutions of hydrochloric acid in two different concentrations. One solution has 10 moles per liter; the other has 2.5 moles per liter. She mixes x liters of the first solution and y liters of the second solution. a. How many moles of acid are in x liters of the first solution? ___________ b. How many moles of acid are in y liters of the second solution? ___________ c. How many moles of acid are in the mixture? _____________________ d. The chemist wants to have 6 moles of acid in the final mixture. She uses 1 liter of the second solution. How many liters of the first solution should she use? ___________ 4. Card Carriers charges $36 to print 1200 business cards and $56 for 2700 cards. Assume the relationship between the price and the number of business cards is linear. a. Write an equation giving price as a function of the number of cards printed. _____________________ b. Find the set-up cost (the cost of printing 0 cards). ___________ c. Find the cost of printing 6000 cards. ___________ 5. The temperature of an oven is 350 F before being turned off. The temperature drops at a constant rate to 190 F in 20 minutes. a. Convert the rate of change to F per minute. ___________ b. Find how long it takes for the oven to cool to 150 F. ___________ 6. At a produce market, Granny Smith apples are $0.75 a pound and Red Delicious apples are $0.95 a pound. Jim has $9 and buys 3 pounds of Granny Smith apples. Round answers to the nearest pound. a. How many pounds of Red Delicious apples can he buy? ___________ b. If the price of each kind of apple increases $0.11 per pound, how many pounds of Red delicious apples can he buy? ___________ 7. A chemist mixed A ounces of a 30% chlorine solution with B ounces of a 40% chlorine solution. The final mixture contained 18 ounces of chlorine. Write an expression to model this situation. ______________________ 8. Last week, Mr. Chinn sold $20,000 worth of newspaper advertisements and earned $800. The week before, he sold $26,000 worth of advertisements and earned $860. Assume the relationship between Mr. Chinn’s weekly earnings and the value of the advertisements he sells is linear. a. Write an equation giving Mr. Chinn’s weekly earnings as a function of the value of the advertisements he sells. ______________________ b. In this situation, what do the slope and y-intercept mean? c. If in one week, Mr. Chinn sells $30,000 worth of advertisements, how much will he earn? ___________ 9. Mr. Reyes bought 5 pounds of coffee. On the average, he uses one-fifth of a pound a week. a. Write an equation relating the pounds of coffee c he has left after w weeks. ______________________ b. During what week will he likely run out of coffee? ___________ 10. Helene bought L 74-minute recordable CDs at $0.58 each and M 80-minute recordable CDs at $0.95 each. Suppose she spent $12.40 and bought ten 80-minute CDs. How many 74-minute CDs did she buy? ___________ In 11 and 12, consider the following information. On a quiz show, 20 points are given for correct answers to regular questions and 50 points are given for correct answers to bonus questions. 11. If a contestant answers 5 regular questions correctly and 7 bonus questions correctly, how many points does she have? ___________ 12. Suppose a contestant earned 650 points. a. If she answered 13 bonus questions correctly, how many regular questions did she answer correctly? ___________ b. If she answered 25 regular questions correctly, how many bonus questions did she answer correctly? ___________ 13. The Kelvin temperature scale is often used by scientists who work with very cold materials. Water freezes at 32 F or 273 K. Water boils at 212 F or 373 K. What Fahrenheit temperature corresponds to 0 K? ___________