The Three Investments 14) Jill made three investments that yielded \$2,260 as annual interest. Her 7.5% investment was \$7,000 more than the one at 5%, and her 8% investment was \$1,000 less than six times the 5% investment. What was the amount she paid for each of these investments? "x" will be the variable for the 5% investment. We, therefore, will figure the other investments on the bases of that. .05(x) + .075(x + 7,000) + .08(6x - 1,000) = 2260.00 Now move the decimal point two places to the right: 5(x) + 7.5(x + 7,000) + 8(6x - 1,000) = 226,000 Then add: 5x + 7.5x + 52,500 + 48x -8,000 = 226,000 Combine like signs: 60.5x + 44,500 = 226,000 Isolate x to one side of the equal sign by performing the operation of deleting 44,500 from both sides: 60.5x = 181,500 Divide both sides by 60.5 to find the value of x: x = 3,000 We can now plug the value of x into the formula: 5(x) + 7.5(x + 7,000) + 8(6x - 1,000) = 226,000 5% = \$3,000 7.5% = \$10,000 (x + 7,000) 8% = \$17,000 (6x - 1,000) To find the annual interest yield of each one, convert the percents back to decimals by dividing them by 100. Then multiply: Investment Interest Earning 5% divided by 100 = .05 .05 * \$3,000 = \$150.00 7.5% divided by 100 = .075 .075 * \$10,000 = \$750.00 8% divided by 100 = .08 .08 * \$17,000 = \$1,360.00 -------------------- \$30,000 \$2,260.00 We can also divide 2,260 by 30,000 to find out what are average percent rate was for all three investments: 7.53%