Question 770408
Let {{{ a }}} = liters of 30% solution needed
Let {{{ b }}} = liters of 60% solution needed
{{{ .3a }}} = liters of acid in 30% solution
{{{ .6b }}} = liters of acid in 60% solution
----------------------------------
(1) {{{ a + b = 30 }}}
(2) {{{ ( .3a + .6b ) / 30 = .4 }}}
--------------------------
(2) {{{ .3a + .6b = .4*30 }}}
(2) {{{ .3a + .6b = 12 }}}
(2) {{{ 3a + 6b = 120 }}}
--------------------
Multiply both sides of (1) by {{{ 3 }}}
and subtract (1) from (2)
(2) {{{ 3a + 6b = 120 }}}
(1) {{{ -3a - 3b = -90 }}}
{{{ 3b = 30 }}}
{{{ b = 10 }}}
and, since
(1) {{{ a + b = 30 }}}
(1) {{{ a = 20 }}}
--------------
Gabe needs 20 liters of the 30% solution.
He also needs 10 liters of the 60% solution.
--------------
check:
(2) {{{ ( .3a + .6b ) / 30 = .4 }}}
(2) {{{ ( .3*20 + .6*10 ) / 30 = .4 }}}
(2) {{{ ( 6 + 6 ) / 30 = .4 }}}
(2) {{{ 12/30 = .4 }}}
(2) {{{ 12 = .4*30 }}}
(2) {{{ 12 = 12 }}}
OK