Question 1154197
Let {{{ a }}} = gallons of 45% antifreeze needed
Let {{{ b }}} = gallons of 85% antifreeze needed
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(1) {{{ a + b = 40 }}}
(2) {{{ ( .45a + .85b ) / 40 = .75 }}}
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(2) {{{ .45a + .85b = 30 }}}
(2) {{{ 45a + 85b = 3000 }}}
(2) {{{ 9a + 17b = 600 }}}
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Multiply both sides of (1) by {{{9}}} and
subtract (1) from (2)
(2) {{{ 9a + 17b = 600 }}}
(1) {{{ -9a - 9b = -360 }}}
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{{{ 8b = 240 }}}
{{{ b = 30 }}}
and
(1) {{{ a + 30 = 40 }}}
(1) {{{ a = 10 }}}
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10 gallons of 45% antifreeze are needed
30 gallons of 85% antifreeze are needed
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check:
(2) {{{ ( .45a + .85b ) / 40 = .75 }}}
(2) {{{ ( .45*10 + .85*30 ) / 40 = .75 }}}
(2) {{{ ( 4.5 + 25.5 ) / 40 = .75 }}}
(2) {{{ 4.5 + 25.5 = 30 }}}
(2) {{{ 30 = 30 }}}
OK