Question 779078
Let {{{ a }}} = quarts of 25% alcohol solution needed
Let {{{ b }}} = quarts of 75% alcohol solution needed
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(1) {{{ a + b = 40 }}}
(2) {{{ ( .25a + .75b ) / 40 = .7 }}}
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(2) {{{ .25a + .75b = .7*40 }}}
(2) {{{ .25a + .75b = 28 }}}
(2) {{{ 25a + 75b = 2800 }}}
Multiply both sides of (1) by {{{ 25 }}} and subtract
(1) from (2)
(2) {{{ 25a + 75b = 2800 }}}
(1) {{{ -25a - 25b = -1000 }}}
{{{ 50b = 1800 }}}
{{{ b = 36 }}}
and, since
(1) {{{ a + b = 40 }}}
(1) {{{ a = 4 }}}
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4 quarts of 25% alcohol solution are needed
36 quarts of 75% alcohol solution are needed
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check:
(2) {{{ ( .25*4 + .75*36 ) / 40 = .7 }}}
(2) {{{ ( 1 + 27 ) / 40 = .7 }}}
(2) {{{ 28 = .7*40 }}}
(2) {{{ 28 = 28 }}}
OK