Math Quiz #2

Question

A long rectangular banquet table has the same number of people seated on each side and no one seated at the ends. Each person is served either chicken or fish. On one side of the table, 11 people are served chicken and the rest are served fish. On the other side of the table, 5 people are served fish and the rest are served chicken. In all, how many more people were served chicken than fish?

Answer 1

Good problem!

 

First side:  # chicken = 11    # fish = f

2nd side:   # chicken = c      # fish  = 5

 

But equal numbers on each side ⇒ 11 + f = c + 5...Equation A.

 

Total chicken eaters = 11 + c; total fish eaters = 5 + f.

 

The difference is 6 + c - f...excess of chicken eaters over fish eaters...Expression B

 

Algebra on Equation A tells us that 11 - 5 = c - f  so  c-f = 6.

Substitute for c - f (= 6) in Expression B to get # of chicken eaters more than fish eaters;

answer is 12.