Question 896188
Let {{{ a }}} = pounds of high-quality coffee bean needed
Let {{{ b }}} = pounds of cheaper coffee bean needed
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(1) {{{ a + b = 150 }}}
(2) {{{ ( 6.25a + 3.5b ) / 150 = 4.97 }}}
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(2) {{{ 6.25a + 3.5b = 4.97*150 }}}
(2) {{{ 6.25a + 3.5b = 745.5 }}}
(2) {{{ 625a + 350b = 74550 }}}
(2) {{{ 25a + 14b = 2982 }}}
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Multiply both sides of (1) by {{{ 14 }}}
and subtract (1) from (2)
(2) {{{ 25a + 14b = 2982 }}}
(1) {{{ -14a - 14b = -2100 }}}
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{{{ 11a = 882 }}}
{{{ a = 80.182 }}}
and
(1) {{{ a + b = 150 }}}
(1) {{{ b = 150 - 80.182 }}}
(1) {{{ b = 69.818 }}}
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80.182 pounds of high-quality coffee bean are needed
69.818 pounds of cheaper coffee bean are needed
check:
(2) {{{ ( 6.25*80.182 + 3.5*69.818 ) / 150 = 4.97 }}}
(2) {{{ ( 501.138 + 244.363 ) / 150 = 4.97 }}}
(2) {{{ 745.501 / 150 = 4.97 }}}
(2) {{{ 745.501 = 745.5 }}}
OK