Question 304983
Let {{{a}}} = pounds of $.60 candy needed
Let {{{b}}} = pounds of $.80 cent candy needed
given:
(1) {{{a + b = 20}}}
In words:
(cost of each type of candy used)/(pounds of candy used) = (cost of mixture)/(pounds of mixture)
{{{(.6a + .8b)/20 = .75}}}
{{{.6a + .8b = 15}}}
(2) {{{6a + 8b = 150}}}
Multiply both sides of (1) by {{{6}}} and subtract from (2)
(2) {{{6a + 8b = 150}}}
(1) {{{-6a - 6b = 120}}}
{{{2b = 30}}}
{{{b = 15}}}
and, since 
{{{a + b = 20}}}
{{{a = 20 - 15}}}
{{{a = 5}}}
5 pounds of $.60 candy and 15 pounds of $.80 candy are needed
check:
{{{(.6*5 + .8*15)/20 = .75}}}
{{{(3 + 12)/20 = .75}}}
{{{15/20 = .75}}}
{{{15 = 15}}}
OK