Question 1026247
Let {{{ a }}} = gallons of 6% butterfat milk needed
Let {{{ b }}} = gallons of 1% butterfat milk needed
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(1) {{{ a + b = 225 }}}
(2) {{{ ( .06a + .01b ) / 225 = .05 }}}
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(2) {{{ .06a + .01b = .05*225 }}}
(2) {{{ .06a + .01b =11.25 }}}
(2) {{{ 6a + b = 1125 }}}
Subtract (1) from (2)
(2) {{{ 6a + b = 1125 }}}
(1) {{{ -a - b = -225 }}}
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{{{ 5a = 900 }}}
{{{ a = 180 }}}
and
(1) {{{ a + b = 225 }}}
(1) {{{ b = 225 - 180 }}}
(1) {{{ b = 45 }}}
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180 gallons of 6% butterfat milk needed
45 gallons of 1% butterfat milk needed
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(2) {{{ ( .06a + .01b ) / 225 = .05 }}}
(2) {{{ ( .06*180 + .01*45 ) / 225 = .05 }}}
(2) {{{ ( 10.8 + .45 ) / 225 = .05 }}}
(2) {{{ 11.25 = .05*225 }}}
(2) {{{ 11.25 = 11.25 }}}
OK