Question 539307
Let {{{a}}} = kg of $6/kg coffee needed
Let {{{b}}} = kg of $4/kg coffee needed
given:
{{{ 6a }}} = cost of $6 coffee
{{{ 4b }}} = cost of $4 coffee
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(1) {{{ a + b = 30 }}} kg
(2) {{{ ( 6a + 4b )/ 30 = 4.8 }}} dollars
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(2) {{{ 6a + 4b = 144 }}}
(2) {{{ 3a + 2b = 72 }}}
Multiply both sides of (1) by {{{2}}} and
subtract (1) from (2)
(2) {{{ 3a + 2b = 72 }}}
(1) {{{ -2a - 2b = -60 }}}
{{{ a = 12 }}}
and, since
(1) {{{ a + b = 30 }}} 
(1) {{{ b = 18 }}}
12 kg of $6/kg coffee are needed
18 kg of $4/kg coffee are needed
check:
(2) {{{ ( 6a + 4b )/ 30 = 4.8 }}}
(2) {{{ ( 6*12 + 4*18 )/ 30 = 4.8 }}}
(2) {{{ ( 72 + 72 ) / 30 = 4.8 }}}
(2) {{{ 144 = 4.8*30 }}}
(2) {{{ 144 = 144 }}}
OK