Question 1030124
Let {{{ a }}} = ounces of 17% alcohol solution needed
Let {{{ b }}} = ounces of 40% alcohol solution needed
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(1) {{{ a + b = 46 }}}
(2) {{{ ( .17a + .4b ) / 46 = .32 }}}
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(2) {{{ .17a + .4b = 14.72 }}}
(2) {{{ 17a + 40b = 1472 }}}
Multiply both sides of (1) by {{{ 17 }}} and
subtract (1) from (2)
(2) {{{ 17a + 40b = 1472 }}}
(1) {{{ -17a - 17b = -782 }}}
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{{{ 23b = 690 }}}
{{{ b = 30 }}}
and
(1) {{{ a + 30 = 46 }}}
(1) {{{ a = 16 }}}
16 ounces of 17% alcohol solution are needed
30 ounces of 40% alcohol solution are needed
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check:
(2) {{{ ( .17a + .4b ) / 46 = .32 }}}
(2) {{{ ( .17*16 + .4*30 ) / 46 = .32 }}}
(2) {{{ ( 2.72 + 12 ) / 46 = .32 }}}
(2) {{{ 14.72 = .32*46 }}}
(2) {{{ 14.72 = 14.72 }}}
OK