Question 415232
Let {{{a}}} = gallons of $6 syrup needed
Let {{{b}}} = gallons of $.80 syrup needed
given:
(1) {{{a + b = 50}}}
(2) {{{(6a + .8b)/50 = 2.36}}}
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(2) {{{6a + .8b = 118}}} 
(2) {{{60a + 8b = 1180}}}
Multiply both sides of (1) by {{{8}}}
and subtract (1) from (2)
(2) {{{60a + 8b = 1180}}}
(1) {{{-8a - 8b = -400}}}
{{{52a = 780}}}
{{{a = 15}}}
and
(1) {{{a + b = 50}}}
{{{15 + b = 50}}}
{{{b = 35}}}
15 gallons of $6 syrup are needed
35 gallons of $.80 syrup are needed
check answer:
(2) {{{(6a + .8b)/50 = 2.36}}}
(2) {{{(6*15 + .8*35)/50 = 2.36}}}
{{{ (90 + 28)/50 = 2.36}}}
{{{ 118/50 = 2.36}}}
{{{118 = 118}}}
OK