Question 955061
Let {{{ a }}} = liters of 53% alcohol needed
Let {{{ b }}} = liters of 22% alcohol needed
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(1) {{{ a + b = 341 }}}
(2) {{{ ( .53a + .22b ) / 341 = .41 }}}
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(2) {{{ .53a + .22b = 139.81 }}}
(2) {{{ 53a + 22b = 13981 }}}
Multiply both sides of (1) by {{{ 22 }}}
and subtract (1) from (2)
(2) {{{ 53a + 22b = 13981 }}}
(1) {{{ -22a - 22b = -7502 }}}
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{{{ 31a  = 6479 }}}
{{{ a = 209 }}}
and
(1) {{{ a + b = 341 }}}
(1) {{{ 209 + b = 341 }}}
(1) {{{ b = 132 }}}
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209 liters of 53% alcohol are needed
132 liters of 22% alcohol are needed
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check:
(2) {{{ ( .53*209 + .22*132 ) / 341 = .41 }}}
(2) {{{ ( 110.77 + 29.04 ) / 341 = .41 }}}
(2) {{{ 139.81 = 139.81 }}}
OK