Question 492982
Let {{{a}}} = ml of 65% solution needed
Let {{{b}}} = ml of 30% solution needed
given:
{{{ .65a }}} = acid in 65% solution
{{{ .3b }}} = acid in 30% solution
(1) {{{ a + b = 630 }}} ml
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(2) {{{ ( .65a + .3b ) / 630 = .5 }}}
(2) {{{ .65a + .3b = .5*630 }}}
(2) {{{ .65a + .3b = 315 }}}
(2) {{{ 65a + 30b = 31500 }}}
Multiply both sides of (1) by {{{ 30 }}} and subtract (1) from (2)
(2) {{{ 65a + 30b = 31500 }}}
(1) {{{ -30a - 30b = 18900 }}}
{{{ 35a = 12600 }}}
{{{ a = 360 }}}
and, since
(1) {{{ a + b = 630 }}}
(1) {{{ 360 + b = 630 }}}
(1) {{{  b = 270 }}}
360 ml of 65% solution are needed
270 ml of 30% solution are needed
check answer:
(2) {{{ ( .65a + .3b ) / 630 = .5 }}}
(2) {{{ ( .65*360 + .3*270 ) / 630 = .5 }}}
(2) {{{ ( 234 + 81 ) / 630 = .5 }}}
(2) {{{ 315 / 630 = .5 }}}
(2) {{{ 315 = 315 }}}
OK