Answer:
Step-by-step explanation:
Interest earned is proportional to the interest rate, so if the interest earned is the same, the amounts invested must be inversely proportional to the interest rates. That is, for the 3% and 2% accounts, the ratio of money invested is 2:3.
In other words, 2/5 of the money ($3200) was invested at 3%, and 3/5 of the money ($4800) was invested at 2%.
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If you need an equation, you can let x represent the amount invested at the highest rate. Then 8000-x is the amount invested at the lower rate. For the interest in the two accounts to be equal, we have ...
3%·x = 2%·(8000-x) . . . . . the amounts of interest earned are the same
3/2·x = 8000 -x . . . . . . . . divide by 2%
5/2·x = 8000 . . . . . . . . . . . add x and simplify
x = 8000·(2/5) = 3200 . . . multiply by the inverse of the x coefficient
8000-x = 8000 -3200 = 4800 . . . . the amount invested at the lower rate
Tamara invested $3200 in the 3% account and $4800 in the 2% account.
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She earned $96 in each account for the year.
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