Question

for the soccer banquet, the players and their family members selected their favorite main dish and side dish. of the 39 people who chose chicken as the main dish, 18 wanted potatoes. of the 32 people who chose rice as a side dish, 6 chose fish as a main dish. a total of 8 people chose a vegetarian meal with potatoes, and a total of 10 people chose fish as their main dish. which two - way table correctly displays the data?

Explanation:

Step1: Analyze chicken - rice data

We know 39 people chose chicken as main dish and 18 wanted potatoes. So number of people who chose chicken and rice is \(39 - 18=21\).

Step2: Analyze fish - rice data

32 people chose rice as side - dish and 6 chose fish as main dish.

Step3: Analyze vegetarian - potatoes data

8 people chose vegetarian meal with potatoes.

Step4: Analyze fish total data

Total of 10 people chose fish as main dish. So number of people who chose fish and potatoes is \(10 - 6 = 4\).

Now let's check each table:

• In the first table, the number of people who chose chicken and rice is not 21, so it's incorrect.
• In the second table:
• Chicken - rice: Since 39 people chose chicken and 18 chose chicken - potatoes, chicken - rice is \(39 - 18 = 21\).
• Fish - rice: Given 6 people chose fish and rice.
• Vegetarian - potatoes: 8 people.
• Fish total is 10 (6 fish - rice+4 fish - potatoes). This table is correct.
• In the third table, the number of people who chose chicken and rice is not 21, so it's incorrect.
• In the fourth table, the number of people who chose chicken and rice is not 21, so it's incorrect.

Answer:

The second two - way table (with Rice: Chicken 21, Fish 6, Vegetarian 5; Potatoes: Chicken 18, Fish 4, Vegetarian 8; Total: Chicken 39, Fish 10, Vegetarian 13, Total 62)