Question 911579
Let {{{ a }}} = ounces of A needed
Let {{{ b }}} = ounces of B needed
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{{{ .4a }}} = ounces of salt in A
{{{ .65b }}} = ounces of salt in B
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(1) {{{ a + b = 100 }}}
(2) {{{ ( .4a + .65b ) / 100 = .5 }}}
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(2) {{{ .4a + .65b = 50 }}}
Multiply both sides by {{{ 100 }}}
(2) {{{ 40a + 65b = 5000 }}}
Multiply both sides of (1) by {{{ 40 }}}
and subtract (1) from (2)
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(2) {{{ 40a + 65b = 5000 }}}
(1) {{{ -40a - 40b = -4000 }}}
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{{{ 25b = 1000 }}}
{{{ b = 40 }}}
and, since
(1) {{{ a + b = 100 }}}
(1) {{{ a = 60 }}}
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60 ounces of A is needed
40 ounces of B is needed
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check:
(2) {{{ ( .4a + .65b ) / 100 = .5 }}}
(2) {{{ ( .4*60 + .65*40 ) / 100 = .5 }}} 
(2) {{{ ( 24 + 26 ) / 100 = .5 }}}
(2) {{{ 50 = .5*100 }}}
(2) {{{ 50 = 50 }}}
'OK