Question 488190
Let {{{ a }}} = total gallons of gas + oil in the 4% oil mixture
Let {{{ b }}} = total gallons of gas + oil in the 2.5% oil mixture
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given:
The % of gas in the 4% oil mixture is 96%
The % of gas in the 2.5% oil mixture is 97.5%
{{{ 340 + 10 = 350 }}} total gallons of gas + oil in the 2 mixtures
(1) {{{ a + b = 350 }}}
(2) {{{ .96a + .975b = 340 }}}
(3) {{{ .04a + .025b = 10 }}}
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Multiply both sides of (2) and (3) by {{{ 1000 }}}
(1) {{{ a + b = 350 }}}
(2) {{{ 960a + 975b = 340000 }}}
(3) {{{ 40a + 25b = 10000 }}}
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Multiply both sides of (3) by {{{ 39 }}}
and subtract (2) from (3)
(3) {{{ 1560a + 975b = 390000 }}}
(2) {{{ -960a - 975b = -340000 }}}
{{{ 600a = 50000 }}}
{{{ a = 83.333 }}}
and, since
(1) {{{ a + b = 350 }}}
(1) {{{ b = 350 - 83.333 }}}
(1) {{{ b = 266.667 }}}
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{{{ .96a = .96*83.333 }}}
{{{ .96a = 80 }}} gallons
{{{ 83.333 - 80 = 3.333 }}} gallons
and
{{{ .975b = .975*266.667 }}}
{{{ .975b = 260 }}} gallons
{{{ 266.667 - 260 = 6.6667 }}}
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There are 80 gallons of gas in the 4% oil mixture
There are 3 and 1/3 gallons of oil in the 4% oil mixture
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There are 260 gallons of gas in the 2.5% oil mixture
There are 6 and 2/3 gallons of oil in the 2.5% oil mixture
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check:
{{{ 80 + 3 + 1/3 + 260 + 6 + 2/3 = 350 }}}
{{{ 349 + 3/3 = 350 }}}
{{{ 350 = 350 }}}
OK
and {{{ 80 + 260 = 340 }}}
and {{{ 3 + 1/3 + 6 + 2/3 = 10 }}}
OK