Let x be the number of jabs and y be the number of hooks that Rocky throws in 3 minutes.
The total number of punches thrown by Rocky in 3 minutes can be expressed as:
30x + 25y = total punches
The total number of points scored by Rocky in 3 minutes can be expressed as:
x + 2y = total points
Therefore, the system of equations to determine the number of jabs and hooks thrown by Rocky is:
30x + 25y = total punches
x + 2y = total points
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.
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5 answers
Solve the equation
Given that Rocky can throw an average of 30 punches per minute, and he has 3 minutes to throw punches, we can calculate the total number of punches he can throw:
30 punches/minute * 3 minutes = 90 punches
Similarly, Ivan can throw an average of 25 punches per minute, and he also has 3 minutes to throw punches, so the total number of punches he can throw is:
25 punches/minute * 3 minutes = 75 punches
Now we can substitute these total numbers back into the equations to solve for x and y:
30x + 25y = 90 (Equation 1)
x + 2y = 90 (Equation 2)
From Equation 2, we can express x as x = 90 - 2y and substitute it into Equation 1:
30(90 - 2y) + 25y = 90
2700 - 60y + 25y = 90
2700 - 35y = 90
-35y = -2610
y = 74.57
Substitute y back into x = 90 - 2y:
x = 90 - 2(74.57)
x = 90 - 149.14
x = -59.14
Since the number of jabs and hooks must be whole numbers (as you can't throw a fraction of a punch), it seems like there was an error in our calculations. Let me attempt the calculation again:
Given that Rocky throws x jabs and y hooks:
x + y = 90 --> x = 90 - y (Equation 1)
x + 2y = 90 (Equation 2)
Substitute Equation 1 into Equation 2:
90 - y + 2y = 90
y = 90
Substitute y back into Equation 1:
x = 90 - 90
x = 0
Therefore, Rocky throws 0 jabs and 90 hooks to achieve the most points and punches.
30 punches/minute * 3 minutes = 90 punches
Similarly, Ivan can throw an average of 25 punches per minute, and he also has 3 minutes to throw punches, so the total number of punches he can throw is:
25 punches/minute * 3 minutes = 75 punches
Now we can substitute these total numbers back into the equations to solve for x and y:
30x + 25y = 90 (Equation 1)
x + 2y = 90 (Equation 2)
From Equation 2, we can express x as x = 90 - 2y and substitute it into Equation 1:
30(90 - 2y) + 25y = 90
2700 - 60y + 25y = 90
2700 - 35y = 90
-35y = -2610
y = 74.57
Substitute y back into x = 90 - 2y:
x = 90 - 2(74.57)
x = 90 - 149.14
x = -59.14
Since the number of jabs and hooks must be whole numbers (as you can't throw a fraction of a punch), it seems like there was an error in our calculations. Let me attempt the calculation again:
Given that Rocky throws x jabs and y hooks:
x + y = 90 --> x = 90 - y (Equation 1)
x + 2y = 90 (Equation 2)
Substitute Equation 1 into Equation 2:
90 - y + 2y = 90
y = 90
Substitute y back into Equation 1:
x = 90 - 90
x = 0
Therefore, Rocky throws 0 jabs and 90 hooks to achieve the most points and punches.
No decimals
Given that Rocky throws x jabs and y hooks:
x + y = 90 (Equation 1)
x + 2y = 90 (Equation 2)
Subtract Equation 1 from Equation 2:
x + 2y - (x + y) = 90 - 90
y = 0
Substitute y = 0 back into Equation 1:
x + 0 = 90
x = 90
Therefore, Rocky throws 90 jabs and 0 hooks to achieve the most points and punches.
x + y = 90 (Equation 1)
x + 2y = 90 (Equation 2)
Subtract Equation 1 from Equation 2:
x + 2y - (x + y) = 90 - 90
y = 0
Substitute y = 0 back into Equation 1:
x + 0 = 90
x = 90
Therefore, Rocky throws 90 jabs and 0 hooks to achieve the most points and punches.
1 answer