Question 755849
Let {{{ a }}} = pounds of $6/pound coffee needed
Let {{{ b }}} = pounds of $3.50/pound coffee needed
{{{ 6a }}} = cost of $6/pound coffee in blend
{{{ 3.5b }}} = cost of $3.50/pound coffee in blend
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(1) {{{ a + b = 50 }}}
(2) {{{ ( 6a + 3.5b ) / 50 = 4.2 }}}
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(2) {{{  6a + 3.5b = 4.2*50 }}}
(2) {{{  60a + 35b = 2100 }}}
Multiply both sides of (1)  by
{{{ 35 }}} and subtract (1) from (2)
(2) {{{  60a + 35b = 2100 }}}
(1) {{{ -35a - 35b = -1750 }}}
{{{ 25a = 350 }}}
{{{ a = 14 }}}
and, since
(1) {{{ a + b = 50 }}}
(1) {{{ 14 + b = 50 }}}
(1) {{{ b = 36 }}}
14 pounds of $6/pound coffee are needed
36 pounds of $3.50/pound coffee are needed
check:
(2) {{{ ( 6a + 3.5b ) / 50 = 4.2 }}}
(2) {{{ ( 6*14 + 3.5*36 ) / 50 = 4.2 }}}
(2) {{{ ( 84 + 126 ) / 50 = 4.2 }}}
(2) {{{ 210 = 4.2*50 }}}
(2) {{{ 210 = 210 }}}
OK