Question 560098
Let {{{a}}} = gallons of mixture needed from container A
Let {{{b}}} = gallons of mixture needed from container B
{{{ .95a }}} = gallons of gas in container A
{{{ .1B }}} = gallons of gas in container B 
-----------------------
(1) {{{ a + b = 5 }}}
(2) {{{ ( .95a + .1b ) / 5 = .55 }}}
--------------------------
(2) {{{ .95a + .1b = 2.75 }}}
(2) {{{ 95a + 10b = 275 }}}
---------------------
Multiply both sides of (1) by {{{ 10 }}}
and subtract (1) from (2)
(2) {{{ 95a + 10b = 275 }}}
(1) {{{ -10a -10 b = -50 }}}
{{{ 85a = 225 }}}
{{{ a = 2.647 }}}
and, since
(1) {{{ a + b = 5 }}}
(1) {{{ 2.647 + b = 5 }}}
(1) {{{ b = 5 - 2.647 }}}
(1) {{{ b = 2.353 }}}
He needs 2.6 gallons from container A
 and 2.4 gallons from container B
--------
check answer:
(2) {{{ ( .95*2.647 + .1*2.353 ) / 5 = .55 }}}
(2) {{{ ( 2.515 + .235 ) / 5 = .55 }}}
(2) {{{ 2.75 / 5 = .55 }}}
(2) {{{ 2.75 = .55*5 }}}
(2) {{{ 2.75 = 2.75 }}}
OK