Question 705073
Let {{{ a }}} = kg of 45% salt solution needed
Let {{{ b }}} = kg of 75% salt solution needed
given:
(1) {{{ a + b = 15 }}}
(2) {{{ ( .45a + .75b ) / 15 = .67 }}}
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(2) {{{ .45a + .75b = .67*15 }}}
(2) {{{ .45a + .75b = 10.05 }}}
(2) {{{ 45a + 75b = 1005 }}}
Multiply both sides of (1) by {{{ 45 }}}
and subtract (1) from (2)
(2) {{{ 45a + 75b = 1005 }}}
(1) {{{ -45a - 45b = -675 }}}
{{{ 30b = 330 }}}
{{{ b = 11 }}}
and,, since
(1) {{{ a + b = 15 }}}
(1) {{{ a + 11 = 15 }}}
(1) {{{ a = 4 }}}
4 kg of 45% salt solution is needed
11 kg of 75% salt solution is needed
check:
(2) {{{ ( .45a + .75b ) / 15 = .67 }}}
(2) {{{ ( .45*4 + .75*11 ) / 15 = .67 }}}
(2) {{{ ( 1.8 + 8.25 ) / 15 = .67 }}}
(2) {{{ 10.05 / 15 = .67 }}}
(2) {{{ 10.05 = .67*15 }}}
(2) {{{ 10.05 = 10.05 }}}
OK