for the soccer banquet, the players and their family members selected their favorite main dish and side…

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 this data?

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 this data?

Answer

Explanation:

Step1: Analyze chicken - potatoes data

We know 18 people who chose chicken as main dish wanted potatoes.

Step2: Analyze rice - fish data

6 people who chose rice as side - dish chose fish as main dish.

Step3: Analyze vegetarian - potatoes data

8 people chose vegetarian meal with potatoes.

Step4: Analyze fish total data

Total 10 people chose fish as main dish.

Step5: Check row and column totals

For the first table:

  • For the "Rice" row: 18 (chicken - rice)+4 (fish - rice)+8 (vegetarian - rice)=30.
  • For the "Potatoes" row: 21 (chicken - potatoes)+6 (fish - potatoes)+5 (vegetarian - potatoes)=32.
  • For the "Chicken" column: 18 (chicken - rice)+21 (chicken - potatoes)=39.
  • For the "Fish" column: 4 (fish - rice)+6 (fish - potatoes)=10.
  • For the "Vegetarian" column: 8 (vegetarian - rice)+5 (vegetarian - potatoes)=13.
  • Total: 30 + 32=62.

For the second table:

  • For the "Rice" row: 21 (chicken - rice)+6 (fish - rice)+5 (vegetarian - rice)=32.
  • For the "Potatoes" row: 18 (chicken - potatoes)+4 (fish - potatoes)+8 (vegetarian - potatoes)=30.
  • For the "Chicken" column: 21 (chicken - rice)+18 (chicken - potatoes)=39.
  • For the "Fish" column: 6 (fish - rice)+4 (fish - potatoes)=10.
  • For the "Vegetarian" column: 5 (vegetarian - rice)+8 (vegetarian - potatoes)=13.
  • Total: 32 + 30=62. This table satisfies all the given conditions.

For the third table:

  • For the "Rice" row: 14 (chicken - rice)+6 (fish - rice)+19 (vegetarian - rice)=39, but the total number of people who chose rice as side - dish is given as 32, so this is incorrect.

For the fourth table:

  • For the "Potatoes" row: 14 (chicken - potatoes)+6 (fish - potatoes)+19 (vegetarian - potatoes)=39, but the total number of people who chose potatoes as side - dish is given as 32, so this is incorrect.

Answer:

The second two - way table (the one with Rice: Chicken 21, Fish 6, Vegetarian 5, Total 32; Potatoes: Chicken 18, Fish 4, Vegetarian 8, Total 30; Total: Chicken 39, Fish 10, Vegetarian 13, Grand Total 62)