Question 871590
Let {{{ a }}} = ounces of 31% solution needed
Let {{{ b }}} = ounces of 41% solution needed
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(1) {{{ a + b= 40 }}}
(2) {{{ ( .31a + .41b ) / 40  = .4 }}}
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(2) {{{ .31a + .41b = 16 }}}
(2) {{{ 31a + 41b = 1600 }}}
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Multiply both sides of (1) by {{{ 31 }}}
and subtract (1) from (2)
(2) {{{ 31a + 41b = 1600 }}}
(1) {{{ -31a - 31b = -1240 }}}
{{{ 10b = 360 }}}
{{{ b = 36 }}}
and, since
(1) {{{ a + b= 40 }}}
(1) {{{ a = 4 }}}
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4 ounces of 31% solution are needed
36 ounces of 41% solution are needed
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check:
(2) {{{ ( .31a + .41b ) / 40  = .4 }}}
(2) {{{ ( .31*4 + .41*36 ) / 40  = .4 }}}
(2) {{{ ( 1.24 + 14.76 ) / 40 = .4 }}}
(2) {{{ 16/40 = .4 }}}
(2) {{{ 16 = 16 }}}
OK