Question 973749
Let {{{ a }}} = liters of pure acid needed
Let {{{ b }}} = liters of 10% acid solution needed
{{{ .1b }}} = liters of acid in 10% solution
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(1) {{{ ( a + .1b ) / 90 = .22 }}}
(2) {{{ a + b = 90 }}}
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(1) {{{ a + .1b = 19.8 }}}
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Subtract (1) from (2)
(2) {{{ a + b = 90 }}}
(1) {{{ -a - .1b = -19.8 }}}
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{{{ .9b = 70.2 }}}
{{{ b = 78 }}}
and
(2) {{{ a + 78 = 90 }}}
(2) {{{ a = 12 }}}
12 liters of pure acid are needed
78 liters of 10% acid solution are needed
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check:
(1) {{{ ( a + .1b ) / 90 = .22 }}}
(1) {{{ ( 12 + .1*78 ) / 90 = .22 }}}
(1) {{{ ( 12 + 7.8 ) / 90 = .22 }}}
(1) {{{ 19.8 = .22*90 }}}
(1) {{{ 19.8 = 19.8 }}}
OK