Question 598912
Let {{{ a }}} = gallons of 30% mixture needed
Let {{{ b }}} = gallons of 90% mixture needed
given:
{{{ .3a }}} = gallons of ammonia in 30% mixture
{{{ .9a }}} = gallons of ammonia in 90% mixture
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(1) {{{ a + b = 12 }}}
(2) {{{ ( .3a + .9b ) / 12 = .7 }}}
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(2) {{{ .3a + .9b = .7*12 }}}
(2) {{{ .3a + .9b = 8.4 }}}
(2) {{{ 3a + 9b = 84 }}}
Multiply both sides of (1) by {{{ 3 }}} and
subtract (1) from (2)
(2) {{{ 3a + 9b = 84 }}}
(1) {{{ -3a - 3b = -36 }}}
{{{ 6b = 48 }}}
{{{ b = 8 }}}
and, since
(1) {{{ a + b = 12 }}}
(1) {{{ a = 12 - 8 }}}
(1) {{{ a = 4 }}}
8 gallons of the 90% mixture are needed
check:
(2) {{{ ( .3a + .9b ) / 12 = .7 }}}
(2) {{{ ( .3*4 + .9*8 ) / 12 = .7 }}}
(2) {{{ 1.2 + 7.2 = .7*12 }}}
(2) {{{ 8.4 = 8.4 }}}
OK