Question 516150
Let {{{a}}} = miles driven in city
Let {{{b}}} = miles driven on highway
given:
(1) {{{ a + b = 675 }}}
(2) {{{ a/60 + b/51 = 12 }}}
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Multiply both sides of (2) by {{{ 60*51 }}}
(2) {{{ 51a + 60b = 12*60*51 }}}
(2) {{{ 51a + 60b = 36720 }}}
Multiply both sides of (1) by {{{ 51 }}}
and subtract (1) from (2)
(2) {{{ 51a + 60b = 36720 }}}
(1) {{{ -51a - 51b = -34425 }}}
{{{ 9b = 2295 }}}
{{{ b = 255 }}}
and, since
(1) {{{ a + b = 675 }}}
(1) {{{ a = 675 - 255 }}}
(1) {{{ a = 420 }}}
420 miles are driven in city
255 miles are driven on highway
check answer:
(2) {{{ a/60 + b/51 = 12 }}}
(2) {{{ 420/60 + 255/51 = 12 }}}
(2) {{{ 7 + 5 = 12 }}}
(2) {{{ 12 = 12 }}}
OK