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x : y = 8:5

Say I subtract a value of 400 from x and 300 from y, so that:

x-400 : y-300 = 8:3

How do I determine the value of x and y?

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You cross multiply the ratios to get $5x=8y, 3(x-400)=8(y-300)$. Now solve the first equation for one of the variables, plug that into the second and you have one equation in one variable. In this case it will be linear.

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