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Cube Numbers

A ratio of tw...

Question

A ratio of two numbers is 2/3.If 2 is subtracted from the first and 8 from the second, the ratio becomes the reciprocal of the original ratio. Find the numbers.

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Solution

2:3 can be written as 2/3
now 2/3=2x/3x
2x-2/3x-8=3/2
2(2x-2)=3(3x-8
4x-4=9x-24
4x=9x-20
5x=20
x=4
So numbers are 24=8 and 34=12

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