SOLUTION: Two investments totaling $38,500 produce an annual income of $2805. One investment yields 3% per year, while the other yields 9% per year. How much is invested at each rate?

Question 904176: Two investments totaling $38,500 produce an annual income of $2805. One investment yields 3% per year, while the other yields 9% per year. How much is invested at each rate?
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
We know the total amount of money invested. $38500
x+y=38500,
We know that the total interest for the year for the two accounts is $2805
0.03*x+0.09*y=2805
x=38500-y
We substitute for x
0.03*(38500-y)+0.09*y=2805
We multiply out
1155-0.03y+0.09*y=2805
We combine like terms.
0.06*y=1650
Isolate y
y=27500 at 9%
x=38500-y
Calculate x
x=11000 at 3%
We check
0.03*11000+0.09*27500=2805
330+2475=2805
2805=2805
Since this statement is TRUE and neither amount is negative then it is ok

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