Question 606141
Let {{{ a }}} = ml of 10% solution needed
Let {{{ b }}} = ml of 15% solution needed
{{{ .1a }}} = ml of salt in 10% solution
{{{ .15b }}} = ml of salt in 15% solution
----------------
(1) {{{ ( .1a + .15b ) / 100 = .12 }}}
(2) {{{ a + b = 100 }}}
----------------
(1) {{{ .1a + .15b = 12 }}}
(1) {{{ 10a + 15b = 1200 }}}
Multiply both sides of (2) by {{{ 10 }}}
and subtract (2) from (1)
(1) {{{ 10a + 15b = 1200 }}}
(2) {{{ -10a - 10b = -1000 }}}
{{{ 5b = 200 }}}
{{{ b = 40 }}}
and, since
(2) {{{ a + b = 100 }}}
(2) {{{ a + 40 = 100 }}}
(2) {{{ a = 100 - 40 }}}
(2) {{{ a = 60 }}}
60 ml of 10% solution is needed
check answer
(1) {{{ ( .1a + .15b ) / 100 = .12 }}}
(1) {{{ ( .1*60 + .15*40 ) / 100 = .12 }}}
(1) {{{  6 + 6 = .12*100 }}}
(1) {{{ 12 = 12 }}}
OK