SOLUTION: donnie invested her $33,000 bonus and received a total of 970.00 in interest after one year. If part of the money returned 4% and the remainder 2.25%, then how much did she invest

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Question 90518This question is from textbook elementary algebra
: donnie invested her $33,000 bonus and received a total of 970.00 in interest after one year. If part of the money returned 4% and the remainder 2.25%, then how much did she invest at each rate? This question is from textbook elementary algebra

Found 2 solutions by checkley75, rossiv53:
Answer by checkley75(3666) (Show Source):
You can put this solution on YOUR website!
.04X+.0225(33000-X)=970
.04X+742.5-.0225X=970
.0175X=970-742.5
.0175X=227.5
X=227.5/.0175
X=13000 INVESTED @ 4%
33000-13000=20000 INVESTED @ 2.25%
PROOF
.04*13000+.0225*20000=970
520+450=970
970=970

Answer by rossiv53(27) (Show Source):
You can put this solution on YOUR website!
You are being asked to find the amounts invested at each rate.
Let x = the amount invested at 4% and y = the amount invested at 2.25%.
Since the total money invested was $33,000, your first equation is x + y =$33,000. Since the total interest is $970, your second equation is 4%x+2.25%y = $970.
Solve the system

Solve the first equation for x. Substitute in the second equation and solve for y.

Then

Now you can solve for x

So, your answer is $13,000 invested at 4% and $20000 invested at %2.25.
You can check the second equation.

checks!
Good Luck!