Question 508940
Let {{{a}}} = pounds of 70% meat needed
Let {{{b}}} = pounds of 30% meat needed
given:
(1) {{{ a + b = 3060 }}} pounds
(2) {{{ (.7a + .3b) / 3060 = .37 }}}
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(2) {{{ .7a + .3b = 1132.2 }}}
(2) {{{ 7a + 3b = 11322 }}}
Multiply both sides of (1) by {{{ 3 }}}
and subtract (1) from (2)
(2) {{{ 7a + 3b = 11322 }}}
(1) {{{ -3a - 3b = -9180 }}}
{{{ 4a = 2142 }}}
{{{ a = 535.5 }}}
and, since
(1) {{{ a + b = 3060 }}}
(1) {{{ b = 3060 - 535.5 }}}
(1) {{{ b = 2524.5 }}}
535.5 pounds of 70% meat are needed
2524.5 pounds of 30% meat are needed
check answer:
(2) {{{ (.7a + .3b) / 3060 = .37 }}}
(2) {{{ (.7*535.5 + .3*2524.5) / 3060 = .37 }}}
(2) {{{ (374.85 + 757.35) / 3060 = .37 }}}
(2) {{{ 1132.2 / 3060 = .37 }}}
(2) {{{ 1132.2 = 1132.2 }}}
OK