Question 1043454
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(a+x-y=b,x/y=c)}}} and you want to solve for x and y.


{{{x/y=c}}}
{{{x=cy}}}
-
substitute for x into the "b" equation and first solve for y.
{{{a+cy-y=b}}}
{{{cy-y=b-a}}}
{{{y(c-1)=b-a}}}
{{{highlight(y=(b-a)/(c-1))}}}


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/y=c}}}
{{{y/x=1/c}}}
{{{y=x/c}}}
-
{{{a+x-y=b}}}
{{{x-y=b-a}}}
{{{x-x/c=b-a}}}--------the substitution for y
{{{x(1-1/c)=b-a}}}
{{{x(c/c-1/c)=b-a}}}
{{{x(c-1)/c=b-a}}}
{{{x=(b-a)(c/(c-1))}}}
{{{highlight(x=c(b-a)/(c-1))}}}-----solved for x