SOLUTION: Divide 56 into two parts such that 3/8 of the greater exceeds 1/4 of the smaller by 6.

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Question 891589: Divide 56 into two parts such that 3/8 of the greater exceeds 1/4 of the smaller by 6.
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
let x = the smaller part
This means 56-x is the smaller
(3/8)(56-x) - (1/4)(x) = 6
multiply each side by 8 to get rid of the fractions
3(56-x) - 2(x) = 48
168 - 3x - 2x = 48
168 - 5x = 48
add -168 to each side
-5x = 48 -168
-5x = -120
divide each side by -5
x = 24
(56 -x ) = 56 - 24 = 32
So the larger is 32 and the smaller is 24
Plugging into our equation,
(3/8)(56-24) -(1/4)(24) ?= 6
(3/8)(32) - 6 ?= 6
12 - 6 ?= 6 , clearly yes