Question 1052044
Let {{{ a }}} = quarts of the .5 % oil
Let {{{ b }}} = quarts of the .75% oil
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(1) {{{ a + b = 250 }}} quarts
(2) {{{ ( .005a + .0075b ) / 250 = .0065 }}}
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(2) {{{ .005a + .0075b = .0065*250 }}}
(2) {{{ .005a + .0075b = 1.625 }}}
(2) {{{ 50a + 75b = 16250 }}}
(2) {{{ 2a + 3b = 650 }}}
Multiply both sides of (1) by {{{ 2 }}}  and 
subtract (1) from (2)
(2) {{{ 2a + 3b = 650 }}}
(1) {{{ -2a - 2b = -500 }}}
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{{{ b = 150 }}}
and
(1) {{{ a + b = 250 }}}
(1) {{{ a + 150 = 250 }}}
(1) {{{ a = 100 }}}
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100 quarts of the .5 % oil are needed
150 quarts of the .75% oil are needed
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(2) {{{ ( .005a + .0075b ) / 250 = .0065 }}}
(2) {{{ ( .005*100 + .0075*150 ) / 250 = .0065 }}}
(2) {{{ ( .5 + 1.125 ) / 250 = .0065 }}}
(2) {{{ 1.625 = 1.625 }}}
OK