Question 1048933
Let {{{ a }}} = gallons of 55% antifreeze needed
Let {{{ b }}} = gallons of 95% antifreeze needed
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(1) {{{ a + b = 160 }}}
(2) {{{ ( .55a + .95b ) / 160 = .85 }}}
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(2) {{{ .55a + .95b = .85*160 }}}
(2) {{{ .55a + .95b = 136 }}}
(2) {{{ 55a + 95b = 13600 }}}
(2) {{{ 11a + 19b = 2720 }}}
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Multiply both sides of (1) by {{{ 11 }}}
and subtract (1) from (2)
(2) {{{ 11a + 19b = 2720 }}}
(1) {{{ -11a - 11b = -1760 }}}
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{{{ 8b = 960 }}}
{{{ b = 120 }}}
and
(1) {{{ a + 120 = 160 }}}
(1) {{{ a = 40 }}}
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40 gallons of 55% antifreeze are needed
120 gallons of 95% antifreeze are needed
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check:
(2) {{{ ( .55a + .95b ) / 160 = .85 }}}
(2) {{{ ( .55*40 + .95*120 ) / 160 = .85 }}}
(2) {{{ ( 22 + 114 ) / 160 = .85 }}}
(2) {{{ 136 = .85*160 }}}
(2) {{{ 136 = 136 }}}
OK