Question 569512
Let {{{ a }}} = liters of 10% solution needed
Let {{{ b }}} = liters of 1% solution needed
{{{ .1a }}} = liters of h. acid in 10% solution
{{{ .01b }}} = liters of h. acid in 1% solution 
given:
(1) {{{ a + b = 12 }}}
(2) {{{ ( .1a + .01b ) / 12 = .045 }}}
----------------------------
(2) {{{ .1a + .01b = .045*12 }}}
(2) {{{ .1a + .01b = .54 }}}
(2) {{{ 10a + b = 54 }}}
Subtract (1) from (2)
(2) {{{ 10a + b = 54 }}}
(1) {{{ -a - b = -12 }}}
{{{ 9a = 42 }}}
{{{ a = 4.667 }}} 
and, since
(1) {{{ a + b = 12 }}}
(1) {{{ 4.667 + b = 12 }}}
(1) {{{ b = 12 - 4.667 }}}
(1) {{{ b = 7.333 }}}
4.667 liters of 10% solution are needed
7.333 liters of 1% solution are needed
check:
(2) {{{ ( .1a + .01b ) / 12 = .045 }}}
(2) {{{ ( .1*4.667 + .01*7.333 ) / 12 = .045 }}}
(2) {{{ ( .4667 + .07333 ) / 12 = .045 }}}
(2) {{{ .54003 / 12 = .045 }}}
(2) {{{ .54003 = .54 }}}
OK- error due to rounding off