Question 1050621
Let {{{ a }}} = liters of pure acid needed
Let {{{ b }}} = liters of 10% acid solution needed
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(1) {{{ a + b = 21 }}}
(2) {{{ ( a + .1b ) / 21 = .4 }}}
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(2) {{{ a + .1b = .4*21 }}}
(2) {{{ a + .1b = 8.4 }}}
(2) {{{ 10a + b = 84 }}}
Subtract (1) from (2)
(2) {{{ 10a + b = 84 }}}
(1) {{{ -a - b = -21 }}}
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{{{ 9a = 63 }}}
{{{ a = 7 }}}
and
(1) {{{ a + b = 21 }}}
(1) {{{ 7 + b = 21 }}}
(1) {{{ b = 14 }}}
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7 liters of pure acid are needed
14 liters of 10% acid solution are needed
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check:
(2) {{{ ( a + .1b ) / 21 = .4 }}}
(2) {{{ ( 7 + .1*14 ) / 21 = .4 }}}
(2) {{{ ( 7 + 1.4 ) / 21 = .4 }}}
(2) {{{ 8.4/21 = .4 }}}
(2) {{{ 8.4 = .4*21 }}}
(2) {{{ 8.4 = 8.4 }}}
OK