SOLUTION: $80 is divided between two men such that one-quarter of one person's share is equal to 1/6 of the other. How much will each man receive?

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Question 910287: $80 is divided between two men such that one-quarter of one person's share is equal to 1/6 of the other. How much will each man receive?
Found 3 solutions by ewatrrr, stanbon, MathLover1:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
x the one person's share: (the other (4/6)x)
x + (4/6)x = 80
(10/6)x = 80
x = 80(6/10)
x = $48 and the other $32 %284%2F6%2948

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
$80 is divided between two men such that one-quarter of one person's share is equal to 1/6 of the other. How much will each man receive?
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Let the shares be "x" and "80-x"::
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Equation:
(1/4)x = (1/6)(80-x)
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Multiply both sides by 12 to get
3x = 2(80-x)
3x = 160-2x
5x = 160
x = 32 (one man's ahare)
80-x = 48 (other man's share)
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Cheers,
Stan H.
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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let's one person's share be x and other person's share y
we know that $80=x%2By ....eq.1

we know that one-quarter (1%2F4) of one person's share (x)is equal to 1%2F6 of the other (y)
so, %281%2F4%29x=%281%2F6%29y .....eq.2

%281%2F4%29x=%281%2F6%29y .....eq.2...solve for x
x=4%281%2F6%29y
x=cross%284%292%281%2Fcross%286%293%29y
x=+%282%2F3%29y ....plug it in eq.1

$80=%282%2F3%29y%2By ....eq.1...solve for y

$80=%282%2F3%29y%2B%283%2F3%29y
$80=%285%2F3%29y
$80%2A3=5y
$240%2F5=y
$highlight%2848=y%29
now find x
x=+%282%2F3%29y
x=+%282%2F3%2948
x=+%282%2A48%29%2F3
x=+96%2F3
highlight%28x=+32%29

check:
$80=x%2By ....eq.1
$80=32%2B48
$80=80
%281%2F4%29x=%281%2F6%29y .....eq.2
%281%2F4%2932=%281%2F6%2948
%281%2Fcross%284%291%29cross%2832%298=%281%2Fcross%286%291%29cross%2848%298
8=8