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Question 274054: I need help in performing the correct steps to get to the answer. I have the solution, just don't think I arrived at it "by the book".
If $10,000 and $4000 are invested such that $1250 in interest is earned in 1 year, and the rate of interest on the larger investment is 2% more than that on the smaller investment, find the rates of interest.
Thanks for the help
T
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you invest 10000 and 4000 for 1 year and the interest earned is 1250.
the rate of interest on the larger investment is 2% more than that earned on the smaller investment.
2% divided by 100% = .02
let x = the interest rate earned on the smaller investment.
x + .02 = the interest rate earned on the larger investment.
your equation is:
(x+.02)*10000 + x*4000 = 1250
you solve for x to get your answer.
simplify your equation to get:
10000*x + .02*10000 + 4000*x = 1250
simplify further to get:
10000*x + 200 + 4000*x = 1250
combine like terms to get:
14000*x + 200 = 1250
subtract 200 from both sides of the equation to get:
14000*x = 1250 - 200
combine like terms to get:
14000*x = 1050
divide both sides of the equation by 14000 to get:
x = 1050/14000
simplify to get:
x = .075
that makes x+.02 equal to .095
10000 * .095 + 4000 * .075 = 950 + 300 = 1250 confirming these values are correct.
interest rate on the larger amount is .095 * 100% = 9.5%
interest rate on the smaller amount is .075 * 100% = 7.5%
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