Question 230945
Let {{{a}}} = quarts of 6% butterfat milk needed
Let {{{b}}} = quarts of 2% butterfat milk needed
given:
{{{a + b = 80}}}
{{{.06a}}} = butterfat in {{{a}}}
{{{.02b}}} = butterfat in {{{b}}}
In words:
(quarts of butterfat in 5% milk)/(total quarts of 5% milk) = 5%
(1) {{{(.06a + .02b)/80 = .05}}}
(2) {{{ a + b = 80}}}
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Multiply both sides of (1) by {{{80}}}
(1) {{{.06a + .02b = .05*80}}}
(1) {{{.06a + .02b = 4}}}
(1) {{{6a + 2b = 400}}}
Multiply both sides of (2) by {{{2}}} and 
subtract from (1)
(1) {{{6a + 2b = 400}}}
(2) {{{-2a - 2b = -160}}}
{{{4a = 240}}}
{{{a = 60}}}
and
{{{a + b = 80}}}
{{{b = 80 - 60}}}
{{{b = 20}}}
60 quarts of 6% milk and 20 quarts of 2% milk are needed
check:
(1) {{{(.06a + .02b)/80 = .05}}}
(1) {{{(.06*60 + .02*20)/80 = .05}}}
(1) {{{(3.6 + .4)/80 = .05}}}
(1) {{{4/80 = .05}}}
(1) {{{.05 = .05}}}
OK