Question 1202412: Maricopa's Success scholarship fund receives a gift of $105000. The money is invested in stocks, bonds, and CDs. CDs pay 3.25% interest, bonds pay 5.7% interest, and stocks pay 11.5% interest. Maricopa Success invests $35000 more in bonds than in CDs. If the annual income from the investments is $7937.50 , how much was invested in each account?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website!
TYPE INT. RATE INVESTED INTEREST
stocks 11.5% 105000-2x-35000
bonds 5.7% x+35000
CD's 3.25% x
TOTAL 105000 7937.5
Read and think how this table corresponds to the written description. Fill-in the missing "interest" quantity information, and setup the total interest equation.
Answer by ikleyn(52778)  (Show Source):
You can put this solution on YOUR website! .
Maricopa's Success scholarship fund receives a gift of $105000.
The money is invested in stocks, bonds, and CDs.
CDs pay 3.25% interest, bonds pay 5.7% interest, and stocks pay 11.5% interest.
Maricopa Success invests $35000 more in bonds than in CDs.
If the annual income from the investments is $7937.50, how much was invested in each account?
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Let x be the amount invested in CDs at 3.25%.
Then the amount invested in bonds at 5.7% is (x+35000) dollars, according to the problem.
The amount invested at 11.5% is the rest (105000 - x - (x+35000)) = 70000-2x dollars.
Next write the total interest equation
0.0325x + 0.057(x+35000) + 0.115*(70000-2x) = 7937.50 dollars.
Simplify and find x
0.0325x + 0.057x - 0.115*(2x) = 7937.50 - 0.057*35000 - 0.115*70000
-0.1405x = -2107.50
x =  = 15000.
ANSWER. $15000 was invested at CD (at 3.25%); $15000+$35000 = $50000 was invested in bonds at 5.7%
and the rest 105000-15000-50000 = 40000 dollars were invested in stocks (at 11.5%).
CHECK. 0.0325*15000 + 0.057*50000 + 0.115*40000 = 7937.50 dollars, total annual interest. ! correct !
Solved, using one single equation in one single unknown.
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