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Question 320305: Investing her bonus. 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? Answer by checkley77
In this solution, where does the -1000 come from in the last line before "proof"
.04X+.0225(33,000-X)=970
.04X+742.5-.0225X=970
.0175X=970-742.5
.0175X=227.5
X=227.5/.0175
X=13,000 INVESTED @ 4%.
33,000-1,000=20,000 INVESTED @ 2.25%.
PROOF:
.04*13,000+.0225*20,000=970
52O+450=970
970=970
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Let x return 4% and let y return 2.25%.
Total money invested is $33,000
Total interest earned is $970.
You get:
x + y = $33,000 (total money)
and you get:
.04*x + .0225*y = 970 (total interest)
You need to solve these 2 equations simultaneously.
Take the first equation and solve for x or y.
Solving for y, you get y = 33000 - x.
Substitute for y in the second equation to get:
.04 * x + .0225 * (33000 - x) = 970
You have now reduced the number of unknowns in the equation to 1 which can be solved.
Simplify to get:
.04 * x + .0225 * 33000 - .0225 * x = 970
Combine like terms to get:
.0175 * x + .0225 * 33000 = 970
Simplify further to get:
.0175 * x + 742.5 = 970
Subtract 742.5 from both sides of the equation to get:
.0175 * x = 227.5
Divide both sides of the equation by .0175 to get:
x = 13000
Since x + y = 33000, that means that y must be equal to 33000 - 13000 which makes y equal to 20000.
You have x = 13000 and y = 20000 which makes x + y = 33000
You have .04*x + .0225 * y becomes .04 * 13000 + .0175 * 20000 which becomes 520 + 450 which makes .04*x + .0225 * y = 970.
Both equations check out with the values of x = 13000 and y = 20000 so you're good.
That $33,000 minus $1,000 must have been a typo.
It was supposed to be $33,000 - $13,000.
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