Question 991103
Let {{{ a}}} = pints of the 35% mixture needed
Let {{{ b }}} = pints of the 75% mixture needed
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(1) {{{ a + b = 40 }}}
(2) {{{ ( .35a + .75b ) / 40 = .6 }}}
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(2) {{{ .35a + .75b = .6*40 }}}
(2) {{{ 35a + 75b = 2400 }}}
Multiply both sides of (1) by {{{ 35 }}}
and subtract (1) from (2)
(2) {{{ 35a + 75b = 2400 }}}
(1) {{{ -35a - 35b = -1400 }}}
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{{{ 40b = 1000 }}}
{{{ b = 25 }}}
and
(1) {{{ a + b = 40 }}}
(1) {{{ a = 15 }}}
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15  pints of the 35% mixture are needed
25  pints of the 75% mixture are needed
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check:
(2) {{{ ( .35a + .75b ) / 40 = .6 }}}
(2) {{{ ( .35*15 + .75*25 ) / 40 = .6 }}}
You can finish this check