Question 659460
Let {{{ a }}} = ml of 50% solution needed
Let {{{ b }}} = ml of 10% solution needed
given:
(1) {{{ a + b = 80 }}}
(2) {{{ ( .5a + .1b ) / 80 = .25 }}}
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(2) {{{ .5a + .1b = .25*80 }}}
(2) {{{ .5a + .1b = 20 }}}
(2) {{{ 5a + b = 200 }}}
Subtract (1) from (2)
(2) {{{ 5a + b = 200 }}}
(1) {{{ -a - b = -80 }}}
{{{ 4a = 120 }}}
{{{ a = 30 }}}
and, since
(1) {{{ a + b = 80 }}}
(1) {{{ 30 + b = 80 }}}
(1) {{{ b = 50 }}}
30 ml of 50% solution are needed
50 ml of 10% solution are needed
check:
(2) {{{ ( .5*30 + .1*50 ) / 80 = .25 }}}
(2) {{{ ( 15 + 5 ) / 80 = .25 }}}
(2) {{{ 20 = .25*80 }}}
(2) {{{ 20 = 20 }}}
OK