"$2500 is invested at 2% interest" so you earn 2500*0.02 = 50 dollars in interest alone in one year.
Let x = amount of money invested at 7%
You will earn 0.07x dollars in interest alone
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Total Interest Earned: 50 + 0.07x
Total Amount Invested: 2500 + x
The ratio of amount earned to amount invested is forced to be 6%
(Total Interest Earned)/(Total Amount Invested) = target rate of return
(50 + 0.07x)/(2500 + x) = 0.06
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Now solve for x
(50 + 0.07x)/(2500 + x) = 0.06
50 + 0.07x = 0.06(2500 + x)
50 + 0.07x = 0.06(2500) + 0.06(x)
50 + 0.07x = 150 + 0.06x
0.07x - 0.06x = 150 - 50
0.01x = 100
x = 100/0.01
x = 10,000
So you need to invest $10,000 at 7% so that the total return of both investments average 6%