Question 1126100
let {{{ a }}} = pounds of granola needed
Let {{{ b }}} = pounds of nuts needed
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(1) {{{ a + b = 9 }}}
(2) {{{ ( 4.5a + 7b ) / 9 = 6 }}}
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(2) {{{ 9a + 14b = 108 }}}
Multiply both sides of (1) by {{{ 9 }}} and
subtract (1) from (2)
(2) {{{ 9a + 14b = 108 }}}
(1) {{{ -9a - 9b = -81 }}}
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{{{ 5b = 27 }}}
{{{ b = 5.4 }}}
and
{{{ a + 5.4 = 9 }}}
{{{ a = 3.6 }}}
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3.6 pounds of granola and 5.4 pounds of nuts are needed
check:
(2) {{{ ( 4.5a + 7b )/9 = 6 }}}
(2) {{{ ( 4.5*3.6 + 7*5.4 )/9 = 6 }}}
(2) {{{ ( 16.2 + 37.8 )/ 9 = 6 }}}
(2) {{{ 54 = 6*9 }}}
(2) {{{ 54 = 54 }}}
OK