Rocky Balboa, the boxing legend, and his rival Ivan Drago decided to have a friendly competition to see who could throw the most punches in a given time period. They agreed to throw a combination of jabs and hooks, with jabs counting as 1 point and hooks counting as 2 points. Rocky can throw an average of 30 punches per minute, while Ivan can throw 25 punches per minute. They each have 3 minutes to throw punches. Rocky wants to throw the most punches and earn the most points in the competition. Write a system of equations that could be used to determine the number of jabs and the number of hooks Rocky throws. Define the variables that you use to write the system.

Question

Rocky Balboa, the boxing legend, and his rival Ivan Drago decided to have a friendly competition to see who could throw the most punches in a given time period. They agreed to throw a combination of jabs and hooks, with jabs counting as 1 point and hooks counting as 2 points. Rocky can throw an average of 30 punches per minute, while Ivan can throw 25 punches per minute. They each have 3 minutes to throw punches. Rocky wants to throw the most punches and earn the most points in the competition. Write a system of equations that could be used to determine the number of jabs and the number of hooks Rocky throws. Define the variables that you use to write the system.

Answer 1

Let's define:

- Let x be the number of jabs Rocky throws.
- Let y be the number of hooks Rocky throws.

The system of equations can be written as:
1. x + y = total punches thrown by Rocky in 3 minutes = 30 punches/minute * 3 minutes = 90 punches
2. x + 2y = total points earned by Rocky in 3 minutes = 90 punches

These equations represent the total number of punches thrown by Rocky and the total points earned by Rocky, respectively. Rocky's goal is to maximize the total number of points earned by throwing the most punches.