Question 842196
Let {{{ a }}} = ounces of acid in 30 ounces of solution
Let {{{ b }}} = ounces of acid in 35 ounces of solution
{{{ 30 + 35 = 65 }}} = ounces of solution in 3rd beaker
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(1) {{{ b/35 = 2*( a/30 ) }}}
(2) {{{ ( a + b ) / 65 = .17 }}}
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(1) {{{ b/35 = 2*( a/30 ) }}}
(1) {{{ b/35 = a/15 }}}
Multiply both sides by {{{ 15*35 }}}
(1) {{{ 15b = 35a }}}
(1) {{{ b = (7/3)*a }}}
and
(2) {{{ a + b = .17*65 }}}
(2) {{{ a + (7/3)*a = 11.05 }}}
(2) {{{ ( 10/3 )*a = 11.05 }}}
(2) {{{ a = .3*11.05 }}}
(2) {{{ a = 3.315 }}}
and
(1) {{{ b = (7/3)*a }}}
(1) {{{ b = (7/3)*3.315 }}}
(1) {{{ b = 7.735 }}}
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The concentration of the 30 ounce solution is:
{{{ a/30 = 3.315/30 }}}
{{{ a/30 = .1105 }}} = 11.05%
The concentration of the 35 ounce solution is:
{{{ b/35 = 7.735/35 }}}
{{{ b/35 = .221 }}} = 22.1%
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check answers:
(1) {{{ b/35 = 2*( a/30 ) }}}
(1) {{{ 7.735/35 = 2*( 3.315/30 ) }}}
(1) {{{ .221 = .221 }}}
and
(2) {{{ ( a + b ) / 65 = .17 }}}
(2) {{{ ( 3.315 + 7.735 ) / 65 = .17 }}}
(2) {{{ .17 = .17 }}}
OK