Question 519758
Let {{{a}}} = liters of 75% solution needed
Let {{{b}}} = liters of 25% solution needed
given:
{{{ .75a }}} = liters of disinfectant in 75% solution
{{{ .25b }}} = liters of disinfectant in 25% solution
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(1) {{{ a + b = 10 }}}
(2) {{{ ( .75a + .25b ) / 10 = .4 }}}
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(2) {{{ .75a + .25b = 4 }}}
(2) {{{ 75a + 25b = 400 }}}
(2) {{{ 3a + b = 16 }}}
Subtract (1) from (2)
(2) {{{ 3a + b = 16 }}}
(1) {{{ -a - b = -10 }}}
{{{ 2a = 6 }}}
{{{ a = 3 }}}
and
(1) {{{ a + b = 10 }}}
(1) {{{ b = 10 - 3 }}}
(1) {{{ b = 7 }}}
3 liters of 75% solution are needed
7 liters of 25% solution are needed
check:
(2) {{{ ( .75a + .25b ) / 10 = .4 }}}
(2) {{{ ( .75*3 + .25*7 ) / 10 = .4 }}}
(2) {{{ ( 2.25 + 1.75 ) / 10 = .4 }}}
(2) {{{ 4 = .4*10 }}}
(2) {{{ 4 = 4 }}}
OK