Question 535962
Let {{{ g }}} = number of guests
Let {{{ f }}} = number of fajita dishes
Let {{{ n }}} = number of nacho plates
Let {{{ r }}} = number of refried bean bowls
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There are half as many fajita dishes as guests
{{{ f = g/2 }}}
There are 1/3 as many nacho plates as guests
{{{ n = g/3 }}}
There are 1/4 as many refried bean bowls as guests
{{{ r = g/4 }}}
and
{{{ f + n + r = 65 }}}
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There are 4 equations and 4 unknowns, so it's solvable
By substitution:
{{{ g/2 + g/3 + g/4 = 65 }}}
Multiply both sides by {{{ 12 }}}
{{{ 6g + 4g + 3g = 780 }}}
{{{ 13g = 780 }}}
{{{ g = 60 }}}
There are 60 guests
check:
{{{ f = 30 }}}
{{{ n = 20 }}}
{{{ r = 15 }}}
{{{ f + n + r = 65 }}}
OK