121 1.2 Applications and Modeling with Linear Equations 31. Alcohol Mixture Aryan wishes to strengthen a mixture from 10% alcohol to 30% alcohol. How much pure alcohol should be added to 7 L of the 10% mixture? 32. Alcohol Mixture How many gallons of pure alcohol should be mixed with 20 gal of a 15% alcohol solution to obtain a mixture that is 25% alcohol? 33. Saline Solution How much water should be added to 8 mL of 6% saline solution to reduce the concentration to 4%? 34. Acid Mixture How much pure acid should be added to 18 L of 30% acid to increase the concentration to 50% acid? Solve each problem. See Example 4. 35. Real Estate Financing Cody sells some property for $240,000. The money will be paid off in two ways: a short-term note at 2% interest and a long-term note at 2.5%. Find the amount of each note if the total annual interest paid is $5500. P Note Amount r Interest Rate (%) t Time (in years) I Interest Paid x 2 1 x10.022112 240,000 - x 2.5 1 1240,000 - x210.0252112 36. Buying and Selling Land Roger bought two plots of land for a total of $120,000. When he sold the first plot, he made a profit of 15%. When he sold the second, he lost 10%. His total profit was $5500. How much did he pay for each piece of land? 37. Retirement Planning In planning her retirement, Kaya deposits some money at 2.5% interest, and twice as much money at 3%. Find the amount deposited at each rate if the total annual interest income is $850. 38. Investing a Building Fund A church building fund has invested some money in two ways: part of the money at 3% interest and four times as much at 2.75%. Find the amount invested at each rate if the total annual income from interest is $2800. 39. Inheritance Zhu inherited $200,000 from her grandmother. She first gave 30% to her favorite charity. She invested some of the rest at 1.5% and some at 4%, earning $4350 interest per year. How much did she invest at each rate? 40. Cookbook Royalties Becky earned $48,000 from royalties on her cookbook. She paid a 28% income tax on these royalties. The balance was invested in two ways: some of it at 3.25% interest and some at 1.75%. The investments produced $904.80 interest per year. Find the amount invested at each rate. (Modeling) Solve each problem. See Examples 5 and 6. 41. Warehouse Club Membership If the annual fee for a warehouse club membership is $100 and the reward rate is 2% on club purchases for the year, then the linear equation y = 100 - 0.02x models the actual annual cost of the membership y, in dollars. Here x represents the annual amount of club purchases, also in dollars. (a) Determine the actual annual cost of the membership if club purchases for the year are $2400. (b) What amount of club purchases would reduce the actual annual cost of the membership to $50? (c) How much would a member have to spend in annual club purchases to reduce the annual membership cost to $0? Land Price Rate of Return (%) Profit (or Loss) x 15% 120,000 - x 10%
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