Question 1025825
Let {{{ a }}} = liters of pure acid needed
Let {{{ b }}} = liters of 10% solution needed
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(1) {{{ a + b = 126 }}}
(2) {{{ ( a + .1b ) / 126 = .2 }}}
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(2) {{{ a + .1b = 25.2 }}}
(2) {{{ 10a + b = 252 }}}
Subtract (1) from (2)
(2) {{{ 10a + b = 252 }}}
(1) {{{ -a - b = -126 }}}
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{{{ 9a = 126 }}}
{{{ a = 14 }}}
and
{{{ a + b = 126 }}}
{{{ b = 126 - 14 }}}
{{{ b = 112 }}}
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14 liters of pure acid are needed
112 liters of 10% solution are needed
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check:
(2) {{{ ( a + .1b ) / 126 = .2 }}}
(2) {{{ ( 14 + .1*112 ) / 126 = .2 }}}
(2) {{{ ( 14 + 11.2 ) / 126 = .2 }}}
(2) {{{ 25.2 = .2*126 }}}
(2) {{{ 25.2 = 25.2 }}}
OK