Question 581161
Let {{{ a }}} = pounds of bluegrass needed
Let {{{ b }}} = pounds of ryegrass needed
given:
(1) {{{ a + b = 204 }}}
(2) {{{ ( 11a + 14b ) / 204 = 12 }}}
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(2) {{{ 11a + 14b = 2448 }}}
Multiply both sides of (1) by {{{ 11 }}}
and subtract (1) from (2)
(2) {{{ 11a + 14b = 2448 }}}
(1) {{{ -11a - 11b = -2244 }}}
{{{ 3b = 204 }}}
{{{ b = 68 }}}
and, since
(1) {{{ a + b = 204 }}}
(1) {{{ a + 68 = 204 }}}
(1) {{{ a = 204 - 68 }}}
(1) {{{ a = 136 }}}
136 pounds of bluegrass is needed
68 pounds of ryegrass is needed
check:
(2) {{{ ( 11a + 14b ) / 204 = 12 }}}
(2) {{{ ( 11*136 + 14*68 ) / 204 = 12 }}}
(2) {{{ ( 1496 + 952 ) / 204 = 12 }}}
(2) {{{ 2448 / 204 = 12 }}}
(2) {{{ 2448 = 12*204 }}}
(2) {{{ 2448 = 2448 }}}
OK