SOLUTION: write a system of two equations in two unknowns for each problem. Solve each system by substitution. Question: Investing her bonus. Donna invested her 33,000 bonus and recieved

Algebra ->  Graphs -> SOLUTION: write a system of two equations in two unknowns for each problem. Solve each system by substitution. Question: Investing her bonus. Donna invested her 33,000 bonus and recieved      Log On


   

Question 201147: write a system of two equations in two unknowns for each problem. Solve each system by substitution.
Question: Investing her bonus. Donna invested her 33,000 bonus and recieved 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?
Answer by nerdybill(7384) About Me  (Show Source):
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Investing her bonus. Donna invested her 33,000 bonus and recieved 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?
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Let x = amount invested at 4%
and y = amount invested at 2.25%
.
From:"Donna invested her 33,000 bonus"
x + y = 33000 (equation 1)
.
From:"a total of $970 in interest after one year"
.04x + .0225y = 970
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Solving equation 1 for y:
x + y = 33000
y = 33000 -x
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Substitute the above into equation 2 and solve for x:
.04x + .0225y = 970
.04x + .0225(33000-x) = 970
.04x + 742.5 -.0225x = 970
.04x -.0225x = 227.5
0.0175x = 227.5
x = $13000 (amount invested at 4%)
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Amount invested at 2.25%
y = 33000 -x = 33000 -13000 = $20000