Question 669328
Let {{{ a }}} = number of quarts they have
Let {{{ b }}} = number of gallons they have
given:
(1) {{{ a = b + 27 }}}
(2) {{{ 5.25a + 16.87b = 2198.91 }}}
------------------------------
(2) {{{ 525a + 1687b = 219891 }}}
and
(1) {{{ a - b = 27 }}}
----------------
Multiply both sides of (1) by {{{ 1687 }}}
and add the equations
(2) {{{ 525a + 1687b = 219891 }}}
(1) {{{ 1687a - 1687b = 45549 }}}
{{{ 2212a = 265440 }}}
{{{ a = 120 }}}
and, since
(1) {{{ a = b + 27 }}}
(1) {{{ b = a - 27 }}}
(1) {{{ b = 120 - 27 }}}
(1) {{{ b = 93 }}}
120 is the number of quarts they have
93 is the  number of gallons they have
check:
(2) {{{ 5.25*120 + 16.87*93 = 2198.91 }}}
(2) {{{ 630 + 1568.91 = 2198.91 }}}
(2) {{{ 2198.91 = 2198.91 }}}
OK