Eric is planning a 7-day resort vacation. He will play golf on four mornings. He also wants to play tennis but can only play tennis on days he does not play croquet. He will play croquet on any day immediately following a day that he plays golf. What is the greatest number of days he can play tennis?

A)2 B)3 C)4 D)5 E)6

Is the answer b? How did you get your answer? Thanks

Someone help please!!!!

4. If you just move golf to the last 4 days of vacation, he only has 3 days to play croquet, and therefore 4 days can be used for tennis.

THANKS

To determine the greatest number of days Eric can play tennis, let's analyze the given conditions step by step:

1. Eric plans to play golf on four mornings. Therefore, he will not be available for tennis on those four days.

2. Eric wants to play tennis, but only on days he does not play croquet. This means that whenever he plays croquet, he will not be able to play tennis on that day.

3. Eric will play croquet on any day immediately following a day he plays golf. This means that if Eric plays golf on Day 1, he will play croquet on Day 2. If he plays golf on Day 3, he will play croquet on Day 4, and so on.

Based on these conditions, we can now determine the maximum number of days Eric can play tennis:

We can assume Eric plays golf on Days 1, 3, 5, and 7.

- On Day 1, Eric plays golf, so he cannot play croquet. Tennis is available on Day 1.

- On Day 2, tennis is available because Eric does not play golf or croquet on Day 2.

- On Day 3, Eric plays golf and cannot play croquet. Therefore, tennis is available on Day 3.

- On Day 4, Eric plays croquet following a day of golf. Tennis is not available on Day 4.

- On Day 5, Eric plays golf, so he cannot play croquet. Tennis is available on Day 5.

- On Day 6, tennis is available because Eric does not play golf or croquet on Day 6.

- On Day 7, Eric plays golf and cannot play croquet. Therefore, tennis is available on Day 7.

Adding up the available days (1, 2, 3, 5, 6, 7), we find that Eric can play tennis on 6 out of the 7 days of his vacation.

Therefore, the correct answer is E) 6, not B) 3.

Let me know if you need any further clarification!