SOLUTION: Separate 800 into three parts, such that the sum of the first, 1/2 of the second, and 2/5 of the third is 400; and the sum of the second, 3/4 of the first, and 1/4 of the third is

Question 1112145: Separate 800 into three parts, such that the sum of the first, 1/2 of the second, and 2/5 of the third is 400; and the sum of the second, 3/4 of the first, and 1/4 of the third is 400.
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

The given information tells us...
(1)
(2)
(3)

Solve the system by first eliminating one variable to reduce the problem to two equations in two variables. With the given coefficients, eliminating y first looks to be the easiest.

; ; -->

; ; --> -->

Adding the last two equations,
-->

Plugging back into earlier equations, x=100 and y=200.

CHECK:

{{(3/4)(100)+200+(1/4)(500) = 75+200+125 = 400}}}

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