SOLUTION: Donna invested her $33,000 bonus and received a total of $970 in interest after one year. If part of the money returned 4% and the remainder 2.25%, then how much did she invest at

Question 165486: Donna invested her $33,000 bonus and received a total of $970 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?
I need some help I am not sure how to work this problem out. Thank you
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
B = bonus = 33000
BI = bonus interest = 970.
X = amount of money invested at .04 interest rate.
Y = amount of money invested at .0225 interest rate.
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(.04*X) + (.0225)*Y = 970 (equation 1)
you have 1 equation with 2 unknowns so you can't solve directly.
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X + Y = 33000 (equation 2)
subtract X from both sides of equation.
Y = 33000 - X
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you can replace Y with (33000-X) in equation 1.
it becomes:
(.04*X) + (.0225)*(33000-X) = 970
now you have 1 equation with 1 unknown so you can solve for X directly.
remove parentheses:
.04*X + .0225*33000 - .0225*X = 970
perform indicated operations:
.04*X + 742.5 - .0225*X = 970
.0175*X + 742.5 = 970
subtract 742.5 from both sides of equation.
.0175*X = 970 - 742.5 = 227.5
divide both sides of equation by .0175.
X = 13000.
Y = 33000 - 13000 = 20000
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she invested 13000 at .04 interest rate (4%) = 520 interest.
she invested 20000 at .0225 interest rate (2.25%) = 450 interest.
total interest = 970.
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