Question 1079510: Hi my name is Carlena, I'm completely stuck on trying to model this word problem into an algebra equation. I'm not sure where to start to even get this equation started. I just know the $10,000, the Saving's Account APR of 2.64%, the Mutual Fund's APR of 8.9%, the time: one year, and wanting to earn $750 is all important. Also, I might need two equations one for the saving's account and one for the mutual fund. How can I turn this word problem into an equation algebraically? Please help, thank you! :)
The word problem: 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 which has been paying an annual percentage rate (APR) of 2.64% and a mutual fund which 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.
Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website! Hi my name is Carlena, I'm completely stuck on trying to model this word problem into an algebra equation. I'm not sure where to start to even get this equation started. I just know the $10,000, the Saving's Account APR of 2.64%, the Mutual Fund's APR of 8.9%, the time: one year, and wanting to earn $750 is all important. Also, I might need two equations one for the saving's account and one for the mutual fund. How can I turn this word problem into an equation algebraically? Please help, thank you! :)
The word problem: 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 which has been paying an annual percentage rate (APR) of 2.64% and a mutual fund which 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.
ONE VARIABLE (EASIER method)
Let the amount invested in the savings account (2.64% interest rate), be S
Then amount invested in the mutual fund is: 10,000 - S
Interest earned, from the savings account, in 1 year: .0264S
Interest earned, from the mutual fund account, in 1 year: .089(10,000 - S)
We then get the following INTEREST-EARNINGS equation: .0264S + .089(10,000 - S) = 750
Solve this for S to get the amount invested in the savings account.
Subtract value for S from 10,000 to get the amount invested in mutual funds.
TWO VARIABLES (MORE DIFFICULT method)
Let the amount invested in the savings account be S, and amount invested in the mutual fund, M
In 1 year, interest earned from the savings account: .0264S
Iin 1 year, interest earned from the mutual fund account: .089M
We then get the following SYSTEM of equations: 
Solve this for S to get the amount invested in the savings account.
Determine value of M to get the amount invested in mutual funds.
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