Math question

Question

Joey Chestnut is trying to break his own world record for eating the most hot dogs and buns in 10 minutes. He needs to eat more than 72 hot dogs to break his record. After 1 minute of competition, Joey has eaten 10 hot dogs. Joey wants to know the number of hot dogs per minute that he needs to eat for the next 9 minutes to break his own record.Let d represent the number of hot dogs Joey eats per minute. Write an inequality to determine the number of hot dogs per minute Joey must eat for the last 9 minutes to break his record.

What is the minimum whole number of hot dogs per minute Joey must eat to break his record?

 

Answer 1

If you count d as the number of hot dogs per minute, 9d would be how many hot dogs he eats in 9 minutes, which is what's left. 

9d + 10 is the expression that shows how many hot dogs he will eat in total: 9d being how much he'll eat in the remaining 9 minutes, and 10 being the number of hot dogs he's already eaten in the first minute.

Since it has to beat his former record of 72, it has to be greater than 72. The inequality would be

9d + 10 > 72

 

Then you can solve for d to find how many he has to eat in the remaining 9 minutes.

9d > 72 - 10

9d > 62

d > 62/9

 

It asks for the minimum WHOLE number of hot dogs he has to eat to break his record. 62/9 is about 6.89, so since d > 6.89, he needs to eat at least 7 hot dogs PER MINUTE in the remaining 9 minutes to beat his old score!