Question 1096495
Let {{{ a }}} = gallons of 10% salt water needed
Let {{{ b }}} = gallons of 25% salt water needed
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(1) {{{ a + b = 10 }}}
(2) {{{ ( .1a + .25b ) / 10 = .2 }}}
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(2) {{{ .1a + .25b = 2 }}}
(2) {{{ 10a + 25b = 200 }}}
(2) {{{ 2a + 5b = 40 }}}
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Multiply both sides of (1) by {{{ 2 }}}
and subtract (1) from (2)
(2) {{{ 2a + 5b = 40 }}}
(1) {{{ -2a -2b = -20 }}}
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{{{ 3b = 20 }}}
{{{ b = 6.667 }}}
and
(1) {{{ a + 6.667 = 10 }}}
(1) {{{ a = 3.333 }}}
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3.333 gallons of 10% salt water needed
6.667 gallons of 25% salt water needed
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check:
(2) {{{ ( .1a + .25b ) / 10 = .2 }}}
(2) {{{ ( .1*3.333 + .25*6.667 ) / 10 = .2 }}}
(2) {{{ ( .3333 + 1.6667 ) / 10 = .2 }}}
(2) {{{ 2/10 = .2 }}}
(2) {{{ .2 = .2 }}}
OK