Question 475262
Let {{{a}}} = gallons of mixture A needed
Let {{{b}}} = gallons of mixture B needed
In words:
(gallons of gasoline in final mixture) / (gallons of final mixture) = 84%
given:
(1) {{{ a + b = 100 }}}
(2) {{{ (.9a + .8b) / 100 = .84 }}}
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From (2),
(2) {{{ .9a + .8b = 84 }}}
(2) {{{ 9a + 8b = 840 }}}
Multiply both sides of (1) by {{{8}}} and subtract from (2)
(2) {{{ 9a + 8b = 840 }}}
(1) {{{ -8a - 8b = -800 }}}
{{{ a = 40 }}}
and
(1) {{{ a + b = 100 }}}
(1) {{{ 40 + b = 100 }}}
(1) {{{ b = 60 }}}
40 gallons of mixture A must be added to 60 gallons of mixture B
check answer:
(2) {{{ (.9a + .8b) / 100 = .84 }}}
(2) {{{ (.9*40 + .8*60) / 100 = .84 }}}
(2) {{{ ( 36 + 48 ) / 100 = .84 }}}
(2) {{{ 84/100 = .84 }}}
OK