Question 713127
Let {{{ a }}} = liters of pure acid needed
Let {{{ b }}} = liters of 10% solution needed
{{{ .1b }}} = liters of pure acid in 10% solution
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(1) {{{ a + b =135 }}}
(2) {{{ ( a + .1b ) / 135 = .2 }}}
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(2) {{{ a + .1b = .2*135 }}}
(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, since
(1) {{{ a + b =135 }}}
(1) {{{ 15 + b =135 }}}
(1) {{{ b = 135 - 15 }}}
(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) {{{ ( 15 + 12 ) / 135 = .2 }}}
(2) {{{ 27 = .2*135 }}}
(2) {{{ 27 = 27 }}}
OK