Question 1091191
Let {{{ a }}} = liters of 50% solution needed
Let {{{ b }}} = liters of 75% solution needed
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(1) {{{ a + b = 60 }}}
(2) {{{ ( .5a + .75b ) / 60 = .6 }}}
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{{{ .5a + .75b = 36 }]]
{{{ 50a + 75b = 3600 }}}
(2) {{{ 2a + 3b = 144 }}}
Multiply both sides of (1) by {{{2}}} and
subtract (1) from (2)
(2) {{{ 2a + 3b = 144 }}}
(1) {{{ -2a -2b = -120 }}}
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{{{ b = 24 }}}
and
(1) {{{ a + 24 = 60 }}}
(1) {{{ a = 36 }}}
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36 liters of 50% solution are needed
24 liters of 75% solution are needed
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check:
{{{ .5a + .75b = 36 }}}
{{{ .5*36 + .75*24 = 36 }}}
{{{ 18 + 18 = 36 }}}
{{{ 36 = 36 }}}
OK