Question 738782
Let {{{ a }}} = gallons of 12% solution needed
Let {{{ b }}} = gallons of 20% solution needed
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(1) {{{ a + b = 40 }}}
(2) {{{ ( .12a + .2b ) / 40 = .15 }}}
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(2) {{{ .12a + .2b = .15*40 }}}
(2) {{{ .12a + .2b = 6 }}}
(2) {{{ 12a + 20b = 600 }}}
Multiply both sides of (1) by {{{ 12 }}}
and subtract (1) from (2)
(2) {{{ 12a + 20b = 600 }}}
(1) {{{ -12a - 12b = -480 }}}
{{{ 8b = 120 }}}
{{{ b = 15 }}}
and, since
(1) {{{ a + b = 40 }}}
(1) {{{ a = 25 }}}
25 gallons of 12% solution are needed
15 gallons of 20% solution are needed
check:
(2) {{{ ( .12*25 + .2*15 ) / 40 = .15 }}}
(2) {{{  3 + 3 = .15*40 }}}
(2) {{{ 6 = 6 }}}
OK