Question 526457
Let {{{a}}} = kgs of $12/kg candy needed
Let {{{b}}} = kgs of $15/kg candy needed
given:
{{{ 12a }}} = cost of $12/kg candy
{{{ 15b }}} = cost of $15/kg candy
{{{ 13*120 = 1560 }}} cost of mixture
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(1) {{{ a + b = 120 }}}
(2) {{{ 12a + 15b  = 1560 }}}
Multiply both sides of (1) by {{{12}}} and
subtract (1) from (2)
(2) {{{ 12a + 15b  = 1560 }}}
(1) {{{ -12a - 12b = 1440 }}}
{{{ 3b = 120 }}}
{{{ b = 40 }}}
and
(1) {{{ a + b = 120 }}}
(1) {{{ a = 120 - 40 }}}
(1) {{{ a = 80 }}}
80 kgs of $12/kg candy are needed
40 kgs of $15/kg candy are needed