SOLUTION: Jill invested $2000, part at 12%/a and the remainder at 8%/a. At the end of one year the amount of interest from each investment were equal. How much was invested at each rate

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Question 1010026: Jill invested $2000, part at 12%/a and the remainder at 8%/a. At the end of one year the amount of interest from each investment were equal. How much was invested at each rate
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
x = part invested at 12%.
y = part invested at 8%.

interest on x = .12x
interest on y = .08y

at the end of the year .12x = .08y

x + y = 2000

several ways to solve.
this is one way.

from .12x = .08y, solve for y to get y = .12x/.08 = 1.5x

in x + y = 2000, replace y with 1.5x to get x + 1.5x = 2000

combine like terms to get 2.5x = 2000

solve for x to get x = 2000 / 2.5 = 800.

since x + y = 2000, y must be equal to 1200

.12*800 = 96

.08*1200 = 96

the interest is equal so the solution is confirmed to be good.

jill invested 800 at 12% and 1200 at 8%.