Question 275882
In words:
(ounces of peanuts in 10% mix + ounces of peanuts in 35% mix)/(ounces of mix) = 20%
Let {{{a}}} = ounces of 10% mix needed
Let {{{b}}} = ounces of 35% mix needed
{{{(.1a + .35b)/8 = .2}}}
(1) {{{a + b = 8}}}
{{{ .1a + .35b = 1.6}}}
(2) {{{10a + 35b = 160}}}
Multiply both sides of (1) by {{{2}}}
and subtract from (2)
(2) {{{10a + 35b = 160}}}
(1) {{{-10a - 10b = -80}}}
{{{25b = 80}}}
{{{b = 3.2}}}
and, since
{{{a + b = 8}}}
{{{a = 8 - 3.2}}}
{{{a = 4.8}}}
4.8 ounces of 10% mix and 3.2 ounces of 35% mix are needed
check:
{{{ .1a + .35b = 1.6}}}
{{{ .1*4.8 + .35*3.2 = 1.6}}}
{{{.48 + 1.12 = 1.6}}}
{{{1.6 = 1.6}}}
OK