Question 963804
S=smaller number;L=larger number
{{{S+L=20}}}
{{{L=20-S}}}
{{{(S)(L)-20=71}}}
{{{(S)(L)=91}}} Substitute for L
{{{(S)(20-S)=91}}}
{{{-S^2+20S=91}}}
{{{-S^2+20S-91=0}}}
{{{S^2-20S+91=0}}}
{{{(S-13)(S-7)=0}}}
{{{S-13=0}}} or {{{S-7=0}}}
{{{S=13}}} or {{{S=7}}}
ANSWER: The smaller number is 7.
CHECK:
{{{((S)(L))-(S+L)=71}}}
{{{((7)(13))-(7+13)=71}}}
{{{91-20=71}}}
{{{71=71}}}