## Country days scholarship rounds receive a gift of $135000. The money is invested in stock, bonds, and CDs. CDs pay 2.75% interest, bonds pay Question Country days scholarship rounds receive a gift of$135000. The money is invested in stock, bonds, and CDs. CDs pay 2.75% interest, bonds pay 4.5% interest, and stocks pay 10.4% interest. Country days invests $70000 more in bonds than CDs. If the annual income from the investments is$8555, how much was invested in stocks, bonds, and CDs?

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3 days 2021-09-13T15:43:38+00:00 1 Answer 0

• CDs — $10,000 • bonds —$80,000
• stocks — $45,000 Step-by-step explanation: Let the variables c, b, s represent the dollar amounts invested in CDs, stocks, and bonds, respectively. Then the problem statement gives us 3 relations between these 3 variables: c + b + s = 135000 . . . . . . . . . . . . . . . . . total invested 0.0275c +.045b +0.104s = 8555 . . . . . total income earned -c + b = 70000 . . . . . . . . . . . . . . . . . . . . . 70,000 more was in bonds than CDs Using the third equation to write an expression for b, we can substitute into the other two equations. b = 70000 +c . . . . . . . . . . . . . . . . expression we can substitute for b c + (70000 +c) +s = 135000 . . . . substitute for b in the first equation 2c +s = 65000 . . . . . . . . . . . . . . . . [eq4] simplify .0275c +.045(70000 +c) +.104s = 8555 . . . . . substitute for b in 2nd eqn .0725c +.104s = 5405 . . . . . . . . . . [eq5] simplify Using [eq4], we can write an expression for s that can be substituted into [eq5]. s = 65000 -2c . . . . . . . expression we can substitute for s 0.0725c +0.104(65000 -2c) = 5405 -0.1355c = -1355 . . . . . . . . . . . . . . . . . . . . subtract 6760, simplify c = 1355/.1355 = 10,000 s = 65000 -2×10000 = 45,000 b = 70000 +10000 = 80,000 The amounts invested in stocks, bonds, and CDs were$45,000, $80,000, and$10,000, respectively.