Question 791999
Let {{{ t }}} = number of hours worked at library
{{{ 25 - t }}} = number of hours worked at construction
--------------
{{{ 8t + 15*( 25 - t ) = 300 }}}
{{{ 8t + 375 - 15t = 300 }}}
{{{ 7t = 375 - 300 }}}
{{{ 7t = 75 }}}
{{{ t = 10.714 }}}
Neglecting fractions of hours, he can work 10 hrs
at library and still earn $300/wk
--------------------
check:
{{{ 8t + 15*( 25 - t ) >= 300 }}}
{{{ 8*10 + 15*( 25 - 10 ) >= 300 }}}
{{{ 80 + 15*15 >= 300 }}}
{{{ 80 + 225 >= 300 }}}
{{{ 325 >= 300 }}}
OK
--------
Suppose he works 11 hrs at library
{{{ 8t + 15*( 25 - t ) >= 300 }}}
{{{ 8*11 + 15*( 25 - 11 ) >= 300 }}}
{{{ 88 + 15*14 >= 300 }}}
{{{ 88 + 210 >= 300 }}}
{{{ 298 >= 300 }}}
This is not true, so he must limit hrs worked
at library to 10 hrs