Question 903962
Let {{{ a }}} = number of small pizzas delivered
Let {{{ b }}} = number of medium pizzas delivered
Let {{{ c }}} = number of large pizzas delivered
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(1) {{{ a + b + c = 16 }}}
(2) {{{ 4a + 9b + 11c = 128 }}}
(3) {{{ 3a + 5b + 10c = 6*16 + 7 }}}
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(3) {{{ 3a + 5b + 10c = 103 }}}
Multiply both sides of (1) by {{{ 3 }}}
and subtract (1) from (3)
(3) {{{ 3a + 5b + 10c = 103 }}}
(1) {{{ -3a - 3b - 3c = -48 }}}
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{{{ 2b + 7c = 55 }}}
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Multiply both sides of (1) by {{{ 4 }}}
and subtract (1) from (2)
(2) {{{ 4a + 9b + 11c = 128 }}}
(1) {{{ -4a - 4b - 4c = -64 }}}
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{{{ 5b + 7c = 64 }}}
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Subtract:
{{{ 5b + 7c = 64 }}}
{{{ -2b - 7c = -55 }}}
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{{{ 3b = 9 }}}
{{{ b = 3 }}}
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and,
{{{ 5*3 + 7c = 64 }}}
{{{ 7c = 64 - 15 }}}
{{{ 7c = 49 }}}
{{{ c = 7 }}}
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(1) {{{ a + b + c = 16 }}}
(1) {{{ a + 3 + 7 = 16 }}}
(1) {{{ a = 6 }}}
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6 small
3 medium
7 large
were delivered