SOLUTION: Ref. Question 1043447: I am not totally clear on the steps to solve for x. Thanks.

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Question 1043454: Ref. Question 1043447:
I am not totally clear on the steps to solve for x. Thanks.
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Question # 10434447: If a is added to the difference of 2 quantities, the sum is b, and if the larger is divided by the smaller, the quotient is c. Determine quantities.

system%28a%2Bx-y=b%2Cx%2Fy=c%29 and you want to solve for x and y.

x%2Fy=c
x=cy
-
substitute for x into the "b" equation and first solve for y.
a%2Bcy-y=b
cy-y=b-a
y%28c-1%29=b-a
highlight%28y=%28b-a%29%2F%28c-1%29%29

You have either of two choices to solve for x. You could use now found y and substitute into either equation, or you could take the ratio equation from the description and solve it for y and then substitute into the "b" equation. I will do this second way.

x%2Fy=c
y%2Fx=1%2Fc
y=x%2Fc
-
a%2Bx-y=b
x-y=b-a
x-x%2Fc=b-a--------the substitution for y
x%281-1%2Fc%29=b-a
x%28c%2Fc-1%2Fc%29=b-a
x%28c-1%29%2Fc=b-a
x=%28b-a%29%28c%2F%28c-1%29%29
highlight%28x=c%28b-a%29%2F%28c-1%29%29-----solved for x