Stock, bond, cd algebra

Question

Maricopa's Success scholarship fund receives a gift of $ 115000. The money is invested in stocks, bonds, and CDs. CDs pay 3.75 % interest, bonds pay 4.1 % interest, and stocks pay 11.9 % interest. Maricopa Success invests $ 40000 more in bonds than in CDs. If the annual income from the investments is $ 8970 , how much was invested in each account? 

Maricopa Success invested $     in stocks.

Maricopa Success invested $     in bonds. 

Maricopa Success invested $     in CDs. 

Answer 1

Let x be the amount of money invested in CDs (Certificates of Deposit). The amount invested in bonds is $40,000 more, so it's x + 40,000. The rest of the $115.000 goes into stocks, so stocks get $115,000 - x - (x+$40,000) = $75,000 - 2x. For simple interest, the interest is equal to the amount you invest times the interest rate in decimal form. Since we have three amounts and three rates, we have:

Interest = CDs·(0.0375) + Bonds·(0.041) + Stocks·(0.119)

8970 = 0.0375x + (0.041)(x+40,000) + (0.119)(75,000 - 2x)

Solve for x. the amount invested in CDs. Use your calculator to help. Once you have the value of x, the amount invested in Bonds is x+ $40,000 and the amount invested in stocks is $75,000 - 2x. Make sure the three add up to $115,000.