Question 731838
Let {{{ a }}} = gallons of 7% milk needed
Let {{{ b }}} = gallons of 4% milk needed
{{{ .07a }}} = gallons of butterfat in 7% milk
{{{ .04b }}} = gallons of butterfat in 4% milk
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(1) {{{ a + b = 270 }}}
(2) {{{ ( .07a + .04b ) / 270 = .06 }}}
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(2) {{{ .07a + .04b = .06*270 }}}
(2) {{{ .07a + .04b = 16.2 }}}
(2) {{{ 7a + 4b = 1620 }}}
Multiply both sides of (1) by {{{ 4 }}}
and subtract (1) from (2)
(2) {{{ 7a + 4b = 1620 }}}
(1) {{{ -4a - 4b = -1080 }}}
{{{ 3a = 540 }}}
{{{ a = 180 }}}
and, since
(1) {{{ a + b = 270 }}}
(1) {{{ b = 270 - 180 }}}
(1) {{{ b = 90 }}}
180 gallons of 7% milk are needed
90 gallons of 4% milk are needed
check:
(2) {{{ ( .07*180 + .04*90 ) / 270 = .06 }}}
(2) {{{ 12.6 + 3.6 = .06*270 }}}
(2) {{{ 16.2 = 16.2 }}}
OK