Question 879396
Let {{{ a }}} = quarts of 6% milk needed
Let {{{ b }}} = quarts of 3% milk needed
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(1) {{{ a + b  = 45 }}}
(2) {{{ ( .06a + .03b ) / 45 = .04 }}}
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(2) {{{ .06a + .03b = 1.8 }}}
(2) {{{ 6a + 3b = 180 }}}
Multiply both sids of (1) by {{{ 3 }}}
and subtract (1) from (2)
(2) {{{ 6a + 3b = 180 }}}
(1) {{{ -3a - 3b = -135 }}}
{{{ 3a = 45 }}}
{{{ a = 15 }}}
and, since
(1) {{{ a + b  = 45 }}}
(1) {{{ b = 45 - 15 }}}
(1) {{{ b = 30 }}}
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15 quarts of 6% milk are needed
30 quarts of 3% milk are needed
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check:
(2) {{{ ( .06a + .03b ) / 45 = .04 }}}
(2) {{{ ( .06*15 + .03*30 ) / 45 = .04 }}}
(2) {{{ ( .9 + .9 ) / 45 = .04 }}}
(2) {{{ 1.8 = .04*45 }}}
(2) {{{ 1.8 = 1.8 }}}
OK