# Math Help - Having trouble getting started on a word problem involving dual APR's

1. ## Having trouble getting started on a word problem involving dual APR's

the question is: "Cathy just won $10,000 in the Oregon state lottery. She wants to put some of the money in an account where it is accessible and to commit the rest to a long-term investment. She has been considering a savings account that has been paying an annual percentage rate (APR) of 2.64% and a mutual fund that has been paying an APR of 8.9%. At the end of one year, Cathy hopes to earn$750. How much money must she invest in each type of account?"

i have manually figured out that $7763.51 must be invested in the 8.9% mutual fund, and$2236.49 must be invested in the 2.64% saving account to yield a profit of $750 on$10,000. The problem is I sort of just ballpark guessed one variable to i narrowed down, and then fine tuned. What would be a systematic and intelligent approach to this problem? thank you

2. x = amount invested @ 2.64%; then 10000-x = amount @ 8.9%
.0264x + .089(10000 - x) = 750
Solve for x

3. ## thx!

thank you so much for pointing me in the right direction!