Question 794667
Let {{{ a }}} = quarts of 7% chocolate milk needed
{{{ .07a }}} = quarts of pure chocolate in 7% chocolate milk
Let {{{ b }}} = quarts of 2% chocolate milk needed
{{{ .02b }}} = quarts of pure chocolate in 2% chocolate milk
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given:
(1) {{{ a + b = 100 }}}
(2) {{{ ( .07a + .02b ) / 100 = .05 }}}
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(2) {{{ .07a + .02b = 5 }}}
(2) {{{ 7a + 2b = 500 }}}
Multiply both sides of (1) by {{{ 2 }}}
and subtract (1) from (2)
(2) {{{ 7a + 2b = 500 }}}
(1) {{{ -2a - 2b = -200 }}}
{{{ 5a = 300 }}}
{{{ a = 60 }}}
and, since
(1) {{{ a + b = 100 }}}
(1) {{{ 60 + b = 100 }}}
(1) {{{ b = 40 }}}
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60 quarts of 7% chocolate milk are needed
40 quarts of 2% chocolate milk are needed 
check answer:
(2) {{{ ( .07a + .02b ) / 100 = .05 }}}
(2) {{{ ( .07*60 + .02*40 ) / 100 = .05 }}}
You can finish this check