Question 752248
Let {{{ a }}} = gallons of 3.6% solution needed
Let {{{ b }}} = gallons of 7% solution needed
{{{ .036a }}} =  gallons of salt in 3.6% solution
{{{ .07b }}} = gallons of salt in 7% solution
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(1) {{{ a + b = 25 }}}
(2) {{{ ( .036a + .07b ) / 25 = .045 }}}
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(2) {{{ ( 36a + 70b ) / 25 = 45 }}}
(2) {{{ 36a + 70b = 1125 }}}
Multiply both sides of (1) by {{{ 36 }}}
and subtract (1) from (2)
(2) {{{ 36a + 70b = 1125 }}}
(1) {{{ -36a - 36b = -900 }}}
{{{ 34b = 225 }}}
{{{ b = 6.618 }}}
and
(1) {{{ a + b = 25 }}}
(1) {{{ a = 18.382 }}}
18.382 gallons of 3.6% solution are needed
6.618 gallons of 7% solution are needed
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check:
(2) {{{ ( .036a + .07b ) / 25 = .045 }}}
(2) {{{ ( .036*18.382 + .07*6.618 ) / 25 = .045 }}}
(2) {{{ ( .6618 + .4633 ) / 25 = .045 }}}
(2) {{{ 1.1251 = .045*25 }}}
(2) {{{ 1.1251 = 1.125 }}}
close enough