A company invests $5000, some into an account paying 5.2% simple interest and the remainder in an account paying 4.5% simple interest per annum. After 2 years the $50000 had grown to $54976. How much went into each account?
At time zero, you have: $\displaystyle (x+y)*50000$
Where $\displaystyle x + y =1 $ as they are percents of the principal that is invested. We'll say x% earns 5.2% simple interest.
After two years we should have:
$\displaystyle x*50000*(1+2*.052) + y*50000*(1+2*.045) = 54976$
Dividing by 50000 gives us:
$\displaystyle 1.104x + 1.09y = 1.09952$
We also know that $\displaystyle x + y =1 $, so now we have two equations with two unknown variables. I believe you can now solve for x and y.