Question 312904
Let {{{a}}} = kilograms of Brazilian coffee needed
Let {{{b}}} = kilograms of Venezuelan coffee needed
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given:
{{{12a}}} = cost of Brazilian coffee in mixture
{{{16b}}} = cost of Venezuelan coffee in mixture
{{{13*384}}} = cost of mixture
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Now I can rite these equations:
{{{12a + 16b = 13*384}}}
(1) {{{12a + 16b = 4992}}}
(2) {{{a + b = 384}}}
Multiply both sides of (2) by {{{12}}} and 
subtract from (1)
(1) {{{12a + 16b = 4992}}}
(2) {{{-12a - 12b = 4608}}}
{{{4b = 384}}}
{{{b = 96}}}
and, since
{{{a + b = 384}}}
{{{a = 384 - 96}}}
{{{a = 288}}}
288 kg of Brazilian coffee and 96 kg of Venezuelan coffee are needed