SOLUTION: solve the extended proportion x/9= 4/y= y/36 for x and y with x>0 and y>0

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Question 887955: solve the extended proportion x/9= 4/y= y/36 for x and y with x>0 and y>0
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F9=+4%2Fy=+y%2F36
36y%28x%2F9=+4%2Fy=+y%2F36%29
4xy=4%2A36=y%5E2
4xy=highlight_green%283%29%2A36 and 4%2A36=y%5E2
The first one is xy=27 and the second one is highlight%28y=12%29; so the first one is x=27/y=27/12, highlight%28x=9%2F4%29. Seems strange.
Maybe a mistake, maybe not. (I found the mistake, outlined in highlight_green%28green%29).

Try differently. Split the three members from the original equation.
x%2F9=4%2Fy
xy=36
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4%2Fy=y%2F36
y%5E2=4%2A36
y=2%2A6
highlight%28y=12%29
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Now back to the first equation again.
xy=36
x=36%2Fy
x=36%2F12
highlight%28x=3%29
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This second solution seems better. You can search for any mistake I must have made in the first method.

CHECK THIS LAST SET OF RESULTS:
3%2F9=4%2F12=12%2F36
1%2F3=1%2F3=1%2F3---Yes, looks good.
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x=3, y=12