Question 610624
Let {{{ a }}} = liters of 15% acid needed
Let {{{ b }}} = liters of 33% acid needed
{{{ .15a }}} = liters of acid in 15% solution
{{{ .33b }}} = liters of acid in 33% solution
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(1) {{{ a + b = 40 }}}
(2) {{{ ( .15a + .33b ) / 40 = .21 }}}
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(2) {{{ .15a + .33b = .21*40 }}}
(2) {{{ .15a + .33b = 8.4 }}}
(2) {{{ 15a + 33b = 840 }}}
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Multiply both sides of (1) by {{{ 15 }}}
and subtract (1) from (2)
(2) {{{ 15a + 33b = 840 }}}
(1) {{{ -15a - 15b = 600 }}}
{{{ 18b = 240 }}}
{{{ b = 13.333 }}} 
and, since
(1) {{{ a + 13.333 = 40 }}}
(1) {{{ a = 26.666 }}} 
26.667 liters of 15% acid are needed
13.333 liters of 33% acid are needed
check:
(2) {{{ ( .15a + .33b ) / 40 = .21 }}}
(2) {{{ ( .15*26.667 + .33*13.333 ) / 40 = .21 }}}
(2) {{{ ( 4.000005 + 4.39989 ) / 40 = .21 }}}
(2) {{{ 8.39994 / 40 = .21 }}}
(2) {{{ 8.39994 = 8.4 }}}
Error must be due to rounding off