890 CHAPTER 9 Systems and Matrices Amount Invested Rate (as a decimal) Annual Interest Real Estate 0.03 Money Market 0.025 CDs 0.015 108. Investment Decisions Jane invests $40,000 received as an inheritance in three parts. With one part she buys mutual funds that offer a return of 2% per year. The second part, which amounts to twice the first, is used to buy government bonds paying 2.5% per year. She puts the rest of the money into a savings account that pays 1.25% annual interest. During the first year, the total interest is $825. How much did she invest at each rate? Amount Invested Rate (as a decimal) Annual Interest Mutual Funds 0.02 Government Bonds 0.025 Savings Account 0.0125 109. Solve the system of equations (4), (5), and (6) from Example 9. 25x + 40y + 20z = 2200 (4) 4x + 2y + 3z = 280 (5) 3x + 2y + z = 180 (6) 110. Check the solution in Exercise 109, showing that it satisfies all three equations of the system. 103. Mixing Water A sparkling-water distributor wants to make up 300 gal of sparkling water to sell for $6.00 per gallon. She wishes to mix three grades of water selling for $9.00, $3.00, and $4.50 per gallon, respectively. She must use twice as much of the $4.50 water as of the $3.00 water. How many gallons of each should she use? 104. Mixing Glue A glue company needs to make some glue that it can sell for $120 per barrel. It wants to use 150 barrels of glue worth $100 per barrel, along with some glue worth $150 per barrel and some glue worth $190 per barrel. It must use the same number of barrels of $150 and $190 glue. How much of the $150 and $190 glue will be needed? How many barrels of $120 glue will be produced? 105. Triangle Dimensions The perimeter of a triangle is 59 in. The longest side is 11 in. longer than the medium side, and the medium side is 3 in. longer than the shortest side. Find the length of each side of the triangle. 106. Triangle Dimensions The sum of the measures of the angles of any triangle is 180°. In a certain triangle, the largest angle measures 55° less than twice the medium angle, and the smallest angle measures 25° less than the medium angle. Find the measures of all three angles. 107. Investment Decisions Carlos receives $200,000 from the sale of a family farm. He invests part of the money in real estate with an annual return of 3% and another part in a money market account at 2.5% interest. He invests the rest, which amounts to $80,000 less than the sum of the other two parts, in certificates of deposit that pay 1.5%. If the total annual interest on the money is $4900, how much was invested at each rate? x + ? x + ? x
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