Course challenge Khan Academy

Question

Joey Chestnut is trying to break his own record for eating the most whole hot dogs in 10 minutes. He needs to eat more than 72 hot dogs to break his record. After 1 minute, Joey has eaten 11 1/4 hot dogs. Let d represent the number of hot dogs Joey eats per minute for the next 9 minutes.

Which inequality represents the number of hot dogs per minute Joey could eat for the last 9 minutes to break his record?

Choose 1 answer:

1. (Choice A)

11 1/4 + 9d>72

1. (Choice B)
2. B
3. 11 1/4 +9d=72
4. (Choice C)
5. C
6. 11 1/4d + 9>72
7. (Choice D)
8. D

11 1/4d+9=72

Will Joey break his record if he eats 666 hot dogs per minute for the next 999 minutes?

Choose 1 answer:

Choose 1 answer:

1. (Choice A)
2. A
3. Yes
4. (Choice B)
5. B
6. No

Answer 1

Hello Sai! To start,

We understand that Joey can eat 11 and 1/4 hot dogs each minute. He has ten minutes total and during the first minute has eaten 11 and 1/4 hot dogs. d is going to represent the number of hot dogs he will eat for the remaining nine minutes of the competition. We also know that he needs to eat more than 72 hot dogs if he wants to break his old record. In order to break his record, he needs to eat a number of hot dogs that is greater than 72, so we will use this symbol >72. We will use this :

9d to represent how many hot dogs he will eat in the remaining nine minutes of his competition. So,

He has already eaten 11 and 1/4 hot dogs. We will add this amount to 9d because 9d represents how many more hot dogs he will eat in the nine minutes he has left.

11 1/4 + 9d > 72

This expression shows how we are adding 11 1/4, the hot dogs he has already eaten in the first minute of the challenge, plus however many hot dogs he eats in nine minutes, 9d, which should be greater than 72, so he can beat 72, his previous number of eaten hot dogs. So, I would choose choice A.

For the second question, we know he can eat 666 hot dogs per minute, and he has 999 minutes. If we multiply

666 x 999 we can find out how many hot dogs he eats in 999 minutes. 666 x 999 = 665,334. This is an absurd number, but if these numbers aren't a typo, this is how many hot dogs Joey can eat in 999 minutes if he is eating at a rate of 666 hot dogs per minute, so for this question, I would choose choice A.