Question 596472
Let {{{ a }}} = ml of 5% solution needed
Let {{{ b }}} = ml of 7% solution needed
{{{ .05a }}} = ml of hydrogen peroxide in 5% solution
{{{ .07b }}} = ml of hydrogen peroxide in 7% solution
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given:
(1) {{{ a + b = 18 }}}
(2) {{{ ( .05a + .07b ) / 18 = .06 }}}
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(2) {{{  .05a + .07b  = .06*18 }}}
(2) {{{  .05a + .07b  = 1.08 }}}
(2) {{{ 5a + 7b = 108 }}}
Multiply both sides of (1) by {{{5}}} and
subtract (1) from (2)
(2) {{{ 5a + 7b = 108 }}}
(1) {{{ -5a - 5b = -90 }}}
{{{ 2b = 18 }}}
{{{ b = 9 }}}
and, since
(1) {{{ a + b = 18 }}}
(1) {{{ a + 9 = 18 }}}
(1) {{{ a = 9 }}}
9 ml of 5% solution is needed
9 ml of 7% solution is needed
check:
(2) {{{ ( .05a + .07b ) / 18 = .06 }}}
(2) {{{ ( .05*9 + .07*9 ) / 18 = .06 }}}
(2) {{{ ( .45 + .63 ) / 18 = .06 }}}
(2) {{{ 1.08 / 18 = .06 }}}
(2) {{{ 1.08 = .06*18 }}}
(2) {{{ 1.08 = 1.08 }}}
OK