SOLUTION: two number have the ratio 3:4 if 5 is subtracted from each of the number the difference have ratio of 1:3 find the number

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Question 1008688: two number have the ratio 3:4 if 5 is subtracted from each of the number the difference have ratio of 1:3 find the number
Found 2 solutions by MathLover1, stanbon:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let numbers be x and y
two number have the ratio x%3Ay=3%3A4 or
x%2Fy=3%2F4....solve for x
x=3y%2F4.........eq.1
if 5 is subtracted from each of the number the difference have ratio of 1%3A3, we have
%28x-5%29%2F%28y-5%29=1%2F3.........substitute x from eq.1
%283y%2F4-5%29%2F%28y-5%29=1%2F3...solve for y, cross multiply first
3%283y%2F4-5%29=1%2A%28y-5%29
9y%2F4-15=y-5
9y%2F4-y=15-5
9y%2F4-4y%2F4=10
5y%2F4=10
5y=40
y=40%2F5
highlight%28y=8%29
go back to x=3y%2F4.........eq.1 substitute in 8 for y
x=3%2A8%2F4
x=3%2Across%288%292%2Fcross%284%29
x=3%2A2
highlight%28x=6%29


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
two number have the ratio 3:4 if 5 is subtracted from each of the number the difference have ratio of 1:3 find the number
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x/y = 3/4
(x-5)/(y-5) = 1/3
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x = (3/4)y
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Substitute for "x" and solve for "y"::
((3/4)y -5)/(y-5) = 1/3
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Cross-multiply::
3[(3/4)y-5] = y-5
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(9/4)y - 15 = y-5
(5/4)y = 10
y = 8
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Solve for "x":
x = (3/4)y
x = (3/4)8 = 6
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Cheers,
Stan H.
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