Question 708691
{{{x}}} = number of jackets were sold before noon (at $31.95 each)
{{{y}}} = number of jackets were sold after noon (at $18.95 each)
All {{{214}}} jackets were sold, so
{{{highlight(x+y=214)}}}
Before noon, the money received for selling {{{x}}} jackets at $31.95 each was
${{{31.95x}}}
After noon, the amount received for selling {{{y}}} jackets at $18.95 each was
${{{18.95y}}}
The total receipts of the clearance sale (all the money received for selling those jackets, in $ was
{{{highlight(31.95x+18.95y=5108.30)}}}
Those two equations form the system
{{{system(x+y=214,31.95x+18.95y=5108.30)}}}
The first equation times 18.95,
{{{18.95x+18.95y=18.95*214}}} --> {{{18.95x+18.95y=4055.30}}}
can be subtracted from the second one to get
{{{31.95x-18.95x=5108.30-4055.30}}} --> {{{13x=1053}}} --> {{{x=1053/13}}} --> {{{highlight(x=81)}}}
That along with {{{x+y=214}}} result in
{{{81+y=214}}} --> {{{y=214-81}}} --> {{{highlight(y=133)}}}