Question 885665
A Small Change:  Suppose that the length L of a certain rectangle is k meters less than m times its width w. The perimeter of the rectangle is p meters. Find the length and width of the rectangle.


p might or might not be an even number.
CONSTANTS:  m, k, p
UNKNOWNS:  L and w
{{{L=mw-k}}} and {{{2w+2L=p}}}


{{{2w+2(mw-k)=p}}} using substitution;
{{{2w+2mw-2k=p}}}
{{{(2+2m)w-2k=p}}}
{{{(2+2m)w=p+2k}}}
{{{highlight(w=(p+2k)/(2+2m))}}}
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Rearrange the L equation, mw=L+k, w=(L+k)/m.
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Substitute w into the perimeter equation:
{{{2(L+k)/m+2L=p}}}
{{{2(L+k)+2mL=mp}}}
{{{2L+2k+2mL=mp}}}
{{{2L+2mL=mp-2k}}}
{{{(2+2m)L=mp-2k}}}
{{{highlight(L=(mp-2k)/(2+2m))}}}