Question 662527
Let {{{ a }}} = liters of 20% solution needed
Let {{{ b }}} = liters of 70% solution needed
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given:
(1) {{{ a + b = 7 }}}
(2) {{{ ( .2a + .7b ) / 7 = .5 }}}
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(2) {{{ .2a + .7b = .5*7 }}}
(2) {{{ 2a + 7b = 35 }}}
Multiply both sides of (1) by {{{2}}}
and subtract (1) from (2)
(2) {{{ 2a + 7b = 35 }}}
(1) {{{ -2a - 2b = -14 }}}
{{{ 5b = 21 }}}
{{{ b = 21/5 }}}
{{{ b = 4.2 }}}
and, since
(1) {{{ a + b = 7 }}}
(1) {{{ a + b = 35/5 }}}
(1) {{{ a + 21/5 = 35/5 }}}
(1) {{{ a = 14/5 }}}
(1) {{{ a = 2.8 }}}
2.8 liters of 20% solution is needed
4.2 liters of 70% solution is needed
check:
(2) {{{ ( .2a + .7b ) / 7 = .5 }}}
(2) {{{ ( .2*2.8 + .7*4.2 ) / 7 = .5 }}}
(2) {{{ ( .56 + 2.94 ) / 7 = .5 }}}
(2) {{{ 3.5 / 7 = .5 }}}
(2) {{{ 3.5 = .5*7 }}}
(2) {{{ 3.5 = 3.5 }}}
OK