Here are the solutions to the problems: Problem 17: Venn Diagram a) 18 guests were served with only one meal, find the value of a. Step 1: Identify the expressions for guests served with only one meal. From the Venn diagram: Guests served only Matooke (M) = $7a - 4$ Guests served only Rice (R) = $5a - 2$ Step 2: Set up the equation based on the given information. The total number of guests served with only one meal is 18. $$(7a - 4) + (5a - 2) = 18$$ Step 3: Solve the equation for $a$. Combine like terms: $$12a - 6 = 18$$ Add 6 to both sides: $$12a = 18 + 6$$ $$12a = 24$$ Divide by 12: $$a = \frac{24}{12}$$ $$a = 2$$ The value of $a$ is $\boxed{2}$. b) Find the total number of guests who attended the party. Step 1: Identify all regions in the Venn diagram. 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 = $3a$ Step 2: Substitute the value of $a=2$ into each expression. 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 = $3(2) = 6$ Step 3: Sum all the values to find the total number of guests. 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 $\boxed{32}$. --- Problem 18: Consecutive Even Numbers a) The sum of three consecutive even numbers is 12. Find the numbers. Step 1: Define the three consecutive even numbers. Let the first even number be $x$. The next consecutive even number is $x+2$. The third consecutive even number is $x+4$. Step 2: Set up the equation based on their sum. $$x + (x+2) + (x+4) = 12$$ Step 3: Solve the equation for $x$. Combine like terms: $$3x + 6 = 12$$ Subtract 6 from both sides: $$3x = 12 - 6$$ $$3x = 6$$ Divide by 3: $$x = \frac{6}{3}$$ $$x = 2$$ Step 4: Find the three numbers. 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. Step 1: Identify the largest and smallest numbers. The numbers are 2, 4, and 6. Largest number = 6 Smallest number = 2 Step 2: Calculate the range. Range = Largest number - Smallest number Range = $6 - 2$ Range = $4$ The range of the numbers is $\boxed{4}$.