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?
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.