Question 1096927
Let {{{ a }}} = number of cheese bought
Let {{{ b }}} = number of pepperoni bought
Let {{{ c }}} = number of supreme bought
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(1) {{{ a + b + c = 35 }}}
(2) {{{ 6a + 9b + 12c = 300 }}}
(3) {{{ 9b = 2*( 6a ) }}}
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Multiply both sides of (1) by {{{ 12 }}} 
and subtract (2) from (1)
(1) {{{ 12a + 12b + 12c = 420 }}}
(2) {{{ -6a - 9b - 12c = -300 }}}
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{{{ 6a + 3b  = 120 }}}
{{{ 2a + b = 40 }}}
and
(3) {{{ 9b = 12a }}}
(3) {{{ b = ( 4/3 )*a }}}
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Using substitution:
{{{ 2a + (4/3)*a = 40 }}}
{{{ (10/3)*a = 40 }}}
{{{ a = (3/10)*40 }}}
{{{ a = 12 }}}
and
{{{ 2a + b = 40 }}}
{{{ 24 + b = 40 }}}
{{{ b = 16 }}}
and
(1) {{{ a + b + c = 35 }}}
(1) {{{ 12 + 16 + c = 35 }}}
(1) {{{ c = 35 - 28 }}}
(1) {{{ c = 7 }}}
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12 cheese
16 pepperoni
7 supreme
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check:
(2) {{{ 6a + 9b + 12c = 300 }}}
(2) {{{ 6*12 + 9*16 + 12*7 = 300 }}}
(2) {{{ 72 + 144 + 84 = 300 }}}
(2) {{{ 300 = 300 }}}
OK