Question

Joey Chestnut is trying to break his own record for eating the most whole hot dogs in 101010 minutes. He needs to eat more than 727272 hot dogs to break his record. After 111 minute, Joey has eaten 11 \dfrac{1}{4}11 4 1 ​ 11, start fraction, 1, divided by, 4, end fraction hot dogs. Let ddd represent the number of hot dogs Joey eats per minute for the next 999 minutes.

Answer 1

Answer:

$9d+11\frac{1}{4}>72$

Step-by-step explanation:

We are supposed to write an inequality to determine the number of hot dogs per minute Joey must eat for the last 9 minutes to break his record.

Let d represent the number of hot dogs Joey eats per minute for the next 9 minutes.

We have been given that after 1 minute, Joey has eaten $11\frac{1}{4}$ hot dogs.

Hot dogs eaten in next 9 minutes would be 9 times d that is $9d$.

Total hot dogs eaten by Joey would be hot dogs eaten in 1 minute plus next 9 minutes: $9d+11\frac{1}{4}$.

Since to break the record Joey needs to eat more than 72 hot dogs. We can represent this information in an inequality as:

$9d+11\frac{1}{4}>72$

Therefore, our required inequality would be $9d+11\frac{1}{4}>72$.