Question 419887
Let {{{a}}} = liters of 80% solution needed
Let {{{b}}} = liters of 30% solution needed
given:
(1) {{{a + b = 400}}} L
acid in final solution is {{{.62*400 = 248}}} L
(2) {{{.8a + .3b = 248}}}
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Multiply both sides of (1) by {{{3}}}
and subtract from (2)
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(2) {{{ 8a +  3b = 2480}}}
(1) {{{-3a - 3b = -1200}}}
{{{ 5a = 1280 }}}
{{{ a = 256 }}}
256 L of 80% solution are needed
check answer:
(2) {{{.8a + .3b = 248}}}
(2) {{{.8*256 + .3b = 248}}}
{{{ 204.8 + .3b = 248 }}}
{{{.3b = 43.2 }}}
{{{b = 144}}}
and
{{{a + b = 400}}}
{{{256 + 144 = 400}}}
{{{ 400 = 400 }}}
OK