Question 896900
Let {{{ a }}} = pounds of $2.75 / lb coffee needed
Let {{{ b }}} = pounds of $5 / lb coffee needed
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{{{ ( 2.75a + 5b ) /( a + b ) = 3.9 }}}
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You need to know the total pounds of coffee to be made
Suppose {{{ 10 }}} pounds is required
(1) {{{ a+ b = 10 }}}
and
(2) {{{ ( 2.75a + 5b ) / 10 = 3.9 }}}
(2) {{{ 2.75a + 5b = 39 }}}
(2) {{{ 275a + 500b = 3900 }}}
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Multiply both sides of (1) by {{{ 275 }}}
and subtract (1) from (2)
(2) {{{ 275a + 500b = 3900 }}}
(1) {{{ -275a - 275b = -2750 }}}
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{{{ 225b = 1150 }}}
{{{ b = 5.111 }}}
and, since
(1) {{{ a+ b = 10 }}}
(1) {{{ a = 4.889 }}}
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4.889 pounds of $2.75 / lb coffee are needed
5.111 pounds of $5 / lb coffee are needed