Question 658021
Let {{{ a }}} = gallons of 18% solution needed
Let {{{ b }}} = gallons of 45% solution needed
given:
(1) {{{ a + b = 12 }}}
(2) {{{ ( .18a + .45b ) / 12 = .36 }}}
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(2) {{{ .18a + .45b = .36*12 }}}
(2) {{{ .18a + .45b = 4.32 }}}
(2) {{{ 18a + 45b = 432 }}}
Multiply both sides of (1) by {{{ 18 }}}
and subtract (1) from (2)
(2) {{{ 18a + 45b = 432 }}}
(1) {{{ -18a - 18b = -216 }}}
{{{ 27b = 216 }}}
{{{ b = 8 }}}
and, since
(1) {{{ a + b = 12 }}}
(1) {{{ a = 12 - 8 }}}
(1) {{{ a = 4 }}}
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4 gallons of 18% solution are needed
8 gallons of 45% solution are needed
check:
(2) {{{ ( .18*4 + .45*8 ) / 12 = .36 }}}
(2) {{{ ( .72 + 3.6 ) / 12 = .36 }}}
(2) {{{ 4.32 = .36*12 }}}
(2) {{{ 4.32 = 4.32 }}}
OK