Question 538171
Let {{{a}}} = ounces of 17% solution needed
Let {{{b}}} = ounces of 39% solution needed
given:
{{{ .17a }}} = ounces of alcohol in 17% solution
{{{ .39b }}} = ounces of alcohol in 39% solution

{{{ .31*88 = 27.28 }}} = ounces of alcohol in final solution
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(1) {{{ a + b = 88 }}}
(2) {{{ ( .17a + .39b ) / 88 = .31 }}}
(2) {{{ .17a + .39b = 27.28 }}}
(2) {{{ 17a + 39b = 2728 }}}
Multiply both sides of (1) by {{{ 17 }}} 
and subtract (1) from (2)
(2) {{{ 17a + 39b = 2728 }}}
(1) {{{ -17a - 17b = -1496 }}} 
{{{ 22b = 1232 }}}
{{{ b = 56 }}}
and, since
(1) {{{ a + b = 88 }}}
(1) {{{ a + 56 = 88 }}}
(1) {{{ a = 32 }}}
32 ounces of 17% solution are needed
56 ounces of 39% solution are needed
check:
(2) {{{ ( .17a + .39b ) / 88 = .31 }}}
(2) {{{ ( .17*32 + .39*56 ) / 88 = .31 }}}
(2) {{{  5.44 + 21.84 = .31*88 }}}
(2) {{{ 27.28 = 27.28 }}}
OK