Question 1047143
Let {{{ a }}} = pounds of high-quality beans needed
Let {{{ b }}} = pounds of cheaper beans needed
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(1) {{{ a + b = 160 }}}
(2) {{{ ( 6.5a + 3.5b ) / 160 = 5.19 }}}
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(2) {{{ 6.5a + 3.5b = 5.19*160 }}}
(2) {{{ 6.5a + 3.5b = 830.4 }}}
(2) {{{ 65a + 35b = 8304 }}}
Multiply both sides of (1) by {{{ 35 }}} and
subtract (1) from (2)
(2) {{{ 65a + 35b = 8304 }}}
(1) {{{ -35a - 35b = -5600 }}}
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{{{ 30a = 2704 }}}
{{{ a = 90.1333 }}}
and
(1) {{{ a + b = 160 }}}
(1) {{{ 90.1333 + b = 160 }}}
(1) {{{ b = 69.8667 }}}
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She needs:
90 pounds of the high quality beans
70 pounds of the cheaper beans
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check:
(2) {{{ ( 6.5a + 3.5b ) / 160 = 5.19 }}}
(2) {{{ ( 6.5*90.133 + 3.5*69.867 ) / 160 = 5.19 }}}
(2) {{{ ( 585.86 + 244.53 ) / 160 = 5.19 }}}
(2) {{{ 830.39 / 160 = 5.19 }}}
(2) {{{ 830.39 = 830.4 }}}
close enough