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Kelly and Justin each win monetary prizes on the TV show US Icon. Kelly immediately deposits her money in an account paying 6.7% effective annual interest, while Justin immediately deposits his in an account paying 5.6% effective annual interest.

After 5 years, they decide to get married, and discover that they have a total of $66440.14 combined in their two accounts. If the sum of their original prizes was $49000, how much did Justin originally win?

I tried using two systems: X+Y=49,000 and Y(1.067^5) + X(1.056^5)= $66440.14

After getting the original in terms of X, I realized there was no easy way to solve the equation. Is there another approach I'm missing or is my algebra off?

CcS
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1 Answers1

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Your system of equations is correct. Try writing the first equation as $X = 49000 - Y$ and substituting that into the second equation (as I think you did), then you get

$$ Y(1.067^5) + (49000-Y)\cdot (1.056^5) = 66440.14 $$

or combining terms

$$ Y(1.067^5 - 1.056^5) + 49000 = 66440.14$$

which is a linear equation in one variable and thus should be easily solved.

aras
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