Question 764479
Let {{{ x }}} = the bill for the meal
before the sales tax is added
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{{{ x + .07x = 1.07x }}} = amount of bill 
after the sales tax is added
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{{{ 1.07x + .2*( 1.07x ) }}} = amount
they paid after including the tip
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Since $50 is the most they can spend,
{{{ 50 = 1.07x + .2*( 1.07x ) }}} 
{{{ 50 = 1.07x*( 1 + .2 ) }}}
{{{ 50 = 1.07*1.2x }}}
{{{ 50 = 1.284x }}}
{{{ x = 38.94 }}}
$38.94 is the most expensive meal they can order
check:
{{{ 1.07*38.94 = 41.67 }}}
{{{ 41.67*1.2 = 50.004 }}}
OK