Question

Joey Chestnut is trying to break his own world record for eating the most hot dogs and buns in 101010 minutes. He needs to eat more than 727272 hot dogs to break his record. After 111 minute of competition, Joey has eaten 101010 hot dogs. Joey wants to know the number of hot dogs per minute that he needs to eat for the next 999 minutes to break his own record.

Answer 1

d = number of hot dogs Joey eats per minute.
(That d is an average rate, and could be a fraction, such as 9 1/2).
Joey has 10-1=9 minutes left.
In that time he will eat
9d hot dogs and buns.

He has already eaten 10 hot dogs and buns.
His total will be 9d+10 hot dogs and buns.
That must be more than 72 , so one inequality to represent the situation is
9d+10>72.

There are other equivalent inequalities:
9d+10>72 <---> 9d>72-10 <---> 9d>62 <---> d>62/9 <---> d>6 8/9