Question 1149424
Let {{{ a }}} = gallons of the 35% antifreeze needed
Let {{{ b }}} = gallons of the 60% antifreeze needed
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(1) {{{ a + b = 160 }}}
(2) {{{ ( .35a + .6b ) / 160 = .45 }}}
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(2) {{{ .35a + .6b = 72 }}}
(2) {{{ 35a + 60b = 7200 }}}
(2) {{{ 7a + 12b = 1440 }}}
Multiply both sides of (1) by {{{ 7 }}} and
subtract (1) from (2)
(2) {{{ 7a + 12b = 1440 }}}
(1) {{{ -7a - 7b = -1120 }}}
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{{{ 5b = 320 }}}
{{{ b = 64 }}}
and
(1) {{{ a + 64 = 160 }}}
(1) {{{ a = 96  }}}
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96 gallons of the 35% antifreeze are needed
64 gallons of the 60% antifreeze are needed
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check:
(2) {{{ ( .35a + .6b ) / 160 = .45 }}}
(2) {{{ ( .35*96 + .6*64 ) / 160 = .45 }}}
(2) {{{ ( 33.6 + 38.4 ) / 160 = .45 }}}
(2) {{{ 72 / 160 = .45 }}}
(2) {{{ .45 = .45 }}}
OK