## Hints for the Language Venn Diagram.

From the first and fifth statement, I have filled in the above numbers.

The second statement gives: ** d + e + f + 4 = 48**

The third statement gives two different equations:
** d = 2 e** and
** d = 4 (4) = 16**

The fourth statement gives: ** a + b + d + 4 = 124**

The sixth statement gives: ** d = 4 + b**

Remember that the total number of students is 208