Question 252427: Can someone please help. I cannot figure out the correct formula.
Using a Linear System to Solve an Application. Jane Hooker invests $40,000 received in 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% a 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 $825.00. How much did she invest at each rate?
Answer: ($10,0000 at 2%; $20,000 at 2.5%; and $10,000 at 1.25%)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! total investment = $40,000
x is invested at 2% per year.
2x is invested at 4.5% per year.
40000 - 3x is invested at 1.25% per year. this represents the rest of the money.
825 is total interest after 1 year.
the formula is:
.02*x + .025*2*x + .0125*(40000-3*x) = 825
simplify by removing parentheses to get:
.02*x + .025*2*x + .0125*40000 - .0125*3*x = 825
simplify further by performing indicated operations to get:
.02*x + .05*x + 500 - .0375*x = 825
simplify further by combining like terms to get:
.0325*x + 500 = 825
subtract 500 from both sides of the equation to get:
.0325*x = 825 - 500 = 325
divide both sides of the equation to get:
x = 325/.0325 = 10,000
2x = 20,000
40,000 - 3x = 40,000 - 30,000 = 10,000
she invested $10,000 at 2% to get $200.00
she invested $20,000 at 2.5% to get $500.00
she invested $10,000 at 1.25% to get $125.00
total interest earned is $200.00 + $500.00 + $125.00 = $825.00 confirming these answers are good.
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