Question 935906
Let {{{ a }}} = liters of pure acid needed
Let {{{ b }}} = liters of 10% solution needed
{{{ .1b }}} = liters of pure acid in 10% solution
-----------------------------------------
(1) {{{ a + b = 135 }}}
(2) {{{ ( a +.1b ) / 135 = .2 }}}
---------------------------
(2) {{{ a + .1b = 27 }}}
(2) {{{ 10a + b = 270 }}}
------------------------
Subtract (1) from (2)
(2) {{{ 10a + b = 270 }}}
(1) {{{ -a - b = -135 }}}
----------------------
{{{ 9a = 135 }}}
{{{ a = 15 }}}
and
(1) {{{ a + b = 135 }}}
(1) {{{ 15 + b = 135 }}}
(1) {{{ b = 120 }}}
-------------------
15 liters of pure acid are needed
120 liters of 10% solution are needed
--------------
check:
(2) {{{ ( a +.1b ) / 135 = .2 }}}
(2) {{{ ( 15 +.1*120 ) / 135 = .2 }}}
(2) {{{ 27/135 = .2 }}}
(2) {{{ 27 = 27 }}}
OK