Question 1155750
Let {{{ a }}} = gallons of $14 water
Let {{{ b }}} = gallons of $3 water
Let {{{ c }}} = gallons of $4.50 water
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(1) {{{ a + b + c = 400 }}}
(2) {{{ ( 14a + 3b + 4.5c ) / 400 = 8 }}}
(3) {{{ c = 2b }}}
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(2) {{{ 14a + 3b + 4.5c = 3200 }}}
(2) {{{ 28a + 6b + 9c = 6400 }}}
Multiply both sides of (1) by {{{ 6 }}} and subtract (1) from (2)
(2) {{{ 28a + 6b + 9c = 6400 }}}
(1) {{{ -6a - 6b -6c = -2400 }}}
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(4) {{{ 22a + 3c = 4000 }}}
Plug (3) into (1)
(1) {{{ a + c/2 + c = 400 }}}
(1) {{{ a + (3/2)*c = 400 }}}
(1) {{{ 2a + 3c = 800 }}}
Subtract (1) from (4)
(4) {{{ 22a + 3c = 4000 }}}
(1) {{{ -2a - 3c = -800 }}}
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{{{ 20a = 3200 }}}
{{{ a = 160 }}}
and
(1) {{{ a + b + c = 400 }}}
(1) {{{ 160 + b + c = 400 }}}
(1) {{{ b + c = 240 }}}
Plug (3) into (1)
(1) {{{ b + 2b = 240 }}}
(1) {{{ 3b = 240 }}}
(1) {{{ b = 80 }}}
and
(1) {{{ a + b + c = 400 }}}
(1) {{{ 160 + 80 + c = 400 }}}
(1) {{{ c = 160 }}}
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160 gallons of $14 water
80 gallons of $3 water
160 gallons of $4.50 water
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check:
(2) {{{ ( 14a + 3b + 4.5c ) / 400 = 8 }}}
(2) {{{ ( 14*160 + 3*80 + 4.5*160 ) / 400 = 8 }}}
(2) {{{ ( 2240 + 240 + 720 ) / 400 = 8 }}}
(2) {{{ 3200 / 400 = 8 }}}
(2) {{{ 3200 = 3200 }}}
OK
check the math & get a 2nd opinion if needed