Question 1077203
Let {{{ t }}} = time in hrs she worked at dentsl office
{{{ 49 - t }}} = time in hrs she worked at shoe store
Let {{{ p }}} = her pay for working that week at dental office
{{{ 506 - p }}} = her pay for working that week at shoe store
--------------------------------------------------------
Equation for the dental office:
(1) {{{ p = 11t }}}
Equation for the shoe store:
(2) {{{ 506 - p = 8*( 49 - t ) }}}
-------------------------------
Substitute (1) into (2)
(2) {{{ 506 - 11t = 8*( 49 - t ) }}}
(2) {{{ 506 - 11t = 392 - 8t }}}
(2) {{{ 3t = 114 }}}
(2) {{{ t = 38 }}}
and
{{{ 49 - t = 49 - 38 }}}
{{{ 49 - t = 11 }}}
She worked 38 hrs at the dental office 
and 11 hrs at the shoe store
----------------------------------------
check:
(1) {{{ p = 11t }}}
(1) {{{ p = 11*38 }}}
(1) {{{ p = 418 }}}
and
(2) {{{ 506 - p = 8*( 49 - t ) }}}
(2) {{{ 506 - p = 8*11 }}}
(2) {{{ p = 506 - 88 }}}
(2) {{{ p = 418 }}}
OK