Question

In a hot dog eating contest, Joey has eaten 15 hot dogs and continues at a rate of eating 5 per minute. Sonia has eaten 21 hot dogs, but now is only eating at a rate of 3 per minute. Which equation represents when each contestant has eaten the same amount of hot dogs?

A. 15m + 5 = 21m + 3
B. 15 + 5m = 21 - 3m
C. 15 - 5m = 21 + 3m
D. 15 + 5m = 21 + 3m

Answer 1

The correct equation to determine when Joey and Sonia have eaten the same number of hot dogs is 15 + 5m = 21 + 3m, which is option D.

Step-by-step explanation:

The question you've asked is related to algebra, specifically linear equations. To determine when Joey and Sonia will have eaten the same number of hot dogs in the hot dog eating contest, we must set up an equation that equates the total number of hot dogs eaten by Joey to the total eaten by Sonia, after a certain number of minutes have passed.

Joey starts with 15 hot dogs and eats 5 more hot dogs per minute. So, the total number of hot dogs Joey has eaten after m minutes is 15 + 5m.

Sonia starts with 21 hot dogs and eats 3 more hot dogs per minute. So, the total number of hot dogs Sonia has eaten after m minutes is 21 + 3m.

To find when they will have eaten the same number of hot dogs, we set Joey's total equal to Sonia's total:

15 + 5m = 21 + 3m

This is the equation that represents when each contestant has eaten the same number of hot dogs. Therefore, the correct answer is option D.