Problem 17: Venn Diagram

From the Venn diagram:
Guests served only Matooke (M) = $7a - 4$
Guests served only Rice (R) = $5a - 2$

The total number of guests served with only one meal is 18.

Combine like terms:

Add 6 to both sides:

Divide by 12:

The value of $a$ is $\boxed{2}$.

b) Find the total number of guests who attended the party.

Guests served only Matooke (M) = $7a - 4$
Guests served both Matooke and Rice (M and R) = $4a$
Guests served only Rice (R) = $5a - 2$
Guests served neither meal = $3a$

Guests served only M = $7(2) - 4 = 14 - 4 = 10$
Guests served both M and R = $4(2) = 8$
Guests served only R = $5(2) - 2 = 10 - 2 = 8$
Guests served neither meal = $3(2) = 6$

Total guests = (only M) + (both M and R) + (only R) + (neither)
Total guests = $10 + 8 + 8 + 6$
Total guests = 32

The total number of guests who attended the party is $\boxed{32}$.

: Consecutive Even Numbers

a) The sum of three consecutive even numbers is 12. Find the numbers.

Let the first even number be $x$.
The next consecutive even number is $x+2$.
The third consecutive even number is $x+4$.

Combine like terms:

Subtract 6 from both sides:

Divide by 3:

First number: $x = 2$
Second number: $x+2 = 2+2 = 4$
Third number: $x+4 = 2+4 = 6$

The three consecutive even numbers are $\boxed{2, 4, 6}$.
(The phrase "if largest numbers is (m-4)" appears to be an unrelated statement or a typo, as it does not fit the context of finding the numbers whose sum is 12.)

b) Work out their range.

The numbers are 2, 4, and 6.
Largest number = 6
Smallest number = 2

Range = Largest number - Smallest number
Range = $6 - 2$
Range = 4

The range of the numbers is $\boxed{4}$.