Question 731619
Let {{{ a }}} = pounds of apples needed
Let {{{ b }}} = pounds of pears needed
given:
(1) {{{ a + b = 30 }}}
(2) {{{  3.15a + 4.25b = 107.7 }}}
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(2) {{{ 315a + 425b = 10770 }}}
Multiply both sides of (1) by {{{ 315 }}}
and subtract (1) from (2)
(2) {{{ 315a + 425b = 10770 }}}
(1) {{{ -315a - 315b = -9450 }}}
{{{ 110b = 1320 }}}
{{{ b = 12 }}}
and, since
(1) {{{ a + b = 30 }}}
(1) {{{ a = 18 }}}
18 pounds of apples and 12 pounds of pears are needed
check:
(2) {{{ 3.15a + 4.25b = 107.7 }}}
(2) {{{ 3.15*18 + 4.25*12 = 107.7 }}}
(2) {{{ 56.7 + 51 = 107.7 }}}
(2) {{{ 107.7 = 107.7 }}}
OK