Expert: Abe Mantell - 8/29/2010

Question
Sara received $50,000 from a real estate deal. She gave $2000 to charity. She invested part of the remainder in a fund with an annual yield of 16% and the rest in a growth fund with a annual yield of 25%. If she made $6060 on these investments in one year, how much did she invest in each fund?

Answer
Hello Arika,

Let x=the amount from the remaining $48,000 Sara invested at 16%
then $48,000-x is the amount she invested at 25%.  Thus, she made
16% of x + 25% of $48,000-x which sums to $6060.  The equation
which expresses this is:
0.16x+0.25(48000-x)=6060, now solve for x
0.16x+12000-0.25x=6060
-0.09x=-5940
x=66000 = $66,000

Since this result is graeter than $48,000, this tells us the problem
has no solution!  It is not possible to earn *only* $6060 in the way
described.  If she invested the entire $48,000 at the lower rate (16%) she would have made $7680.

See?

Abe