SOLUTION: How many guest were present at a Mexican fiesta if every two guest shared fajitas, every three guest shared a plate of nachos,every four guest shared a bowl of refried beans, and t

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Question 535962: How many guest were present at a Mexican fiesta if every two guest shared fajitas, every three guest shared a plate of nachos,every four guest shared a bowl of refried beans, and there were 65 dishes all together?
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Let = number of guests
Let = number of fajita dishes
Let = number of nacho plates
Let = number of refried bean bowls
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There are half as many fajita dishes as guests

There are 1/3 as many nacho plates as guests

There are 1/4 as many refried bean bowls as guests

and

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There are 4 equations and 4 unknowns, so it's solvable
By substitution:

Multiply both sides by

There are 60 guests
check:

OK