Karen baked desserts for a charity fund-raiser. She made 8 pies, 2 cakes, and 2 batches of cookies. She never baked more than two desserts in any 1 day, and she never made two of the same dessert in 1 day. What is the highest number of desserts that Karen could have made in 5 days?

a. 8
b. 9
c. 10
d. 11
e. 12

please answer and explain

To find the highest number of desserts that Karen could have made in 5 days, we need to consider the maximum number of desserts she can make each day without duplicating any dessert.

To start, let's figure out the maximum number of desserts she can make in a single day. Since Karen never baked more than two desserts in any 1 day, the options are:

1. 1 pie
2. 1 cake
3. 1 batch of cookies

Therefore, she can make a maximum of 3 desserts in a single day.

Now, let's see how many total desserts she can make in 5 days.

In the first day, Karen can make three desserts.

On the second day, she can make three more desserts, but she cannot repeat any of the desserts made on the first day. So, she has three new options. Additionally, she can't make more than two desserts in a day, so she can only make two desserts on the second day. This brings the total number of desserts made after the second day to 3 + 2 = 5.

On the third day, she again has three new dessert options, but she cannot repeat any of the desserts made on the first and second days. So, she can make at most two desserts on the third day, bringing the total number of desserts made after the third day to 5 + 2 = 7.

On the fourth day, she has three new dessert options. However, she cannot repeat any of the desserts made on the previous days. Since she has already made 7 desserts, she can only make a maximum of two desserts on the fourth day. This brings the total number of desserts made after the fourth day to 7 + 2 = 9.

On the fifth day, she has three new dessert options, but she has already made 9 desserts. She can only make a maximum of two desserts on the fifth day, bringing the total number of desserts made after the fifth day to 9 + 2 = 11.

Therefore, the highest number of desserts that Karen could have made in 5 days is 11.

The correct answer is d. 11