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. If x represents the number of jabs Rocky throws and y represent the number of hooks he throws, write and solve a system of inequalities graphically and determine one possible solution.
Inequality 1: y ___(put the inequality that best suits for this word problem)
Inequality 2: y ___ (put the inequality that best suits for this word problem.)
Inequality 1: y ≤ 2(3) = 6
Inequality 2: x + y ≤ 30(3) = 90
Now, let's graph these inequalities on a graph:
On the graph, we will have the x-axis representing the number of jabs (x) and the y-axis representing the number of hooks (y).
The first inequality, y ≤ 6, represents the maximum number of hooks Rocky can throw. This forms a horizontal line at y = 6.
The second inequality, x + y ≤ 90, represents the total number of punches Rocky can throw. We can plot this inequality by finding where the line x + y = 90 intersects the axes.
By graphing these two inequalities, we see that the feasible region is a triangle with vertices at (0, 6), (0, 90), and (84, 6).
To find a possible solution, we can test different points within this region. One possible solution is x = 60 and y = 6, which means Rocky would throw 60 jabs and 6 hooks.