A soccer player gets 2 points for a goal and 1 point for an assist. If the combined number of goals and assists that a player has is 24, and the total number of points that the player has is 42, which system of equations can be used to determine the number of goals and assists the player has? Assume [tex]$g$[/tex] represents the number of goals and [tex]$a$[/tex] represents the number of assists.
A. [tex]$g+a=24$[/tex]
[tex]$g+2 a=42$[/tex]
B. [tex]$g+a=24$[/tex]
[tex]$2 g+a=42$[/tex]
C. [tex]$g+a=42$[/tex]
[tex]$g+2 a=24$[/tex]
D. [tex]$g+a=42$[/tex]
[tex]$2 g+a=24$[/tex]
Answer (2)
The system of equations to determine the number of goals and assists for the soccer player is: g + a = 24 and 2 g + a = 42 . The correct answer is option B. This system allows us to calculate the exact number of goals and assists based on the given conditions.
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The problem states that the total number of goals ( g ) and assists ( a ) is 24, which translates to the equation g + a = 24 .
Each goal is worth 2 points and each assist is worth 1 point, and the total points are 42, leading to the equation 2 g + a = 42 .
Combine these two equations to form the system of equations.
The system of equations is { g + a = 24 2 g + a = 42 .
Explanation
Problem Analysis Let's analyze the given information to form the equations. We know that:
A soccer player gets 2 points for a goal ( g ) and 1 point for an assist ( a ).
The combined number of goals and assists is 24.
The total number of points is 42.
We need to create a system of equations to represent this information.
Equation Formation Based on the problem analysis, we can set up the following equations:
The total number of goals and assists is 24, which can be written as:
g + a = 24
The total number of points is 42. Since each goal is worth 2 points and each assist is worth 1 point, this can be written as:
2 g + a = 42
System of Equations Therefore, the system of equations that represents the given information is:
g + a = 24 2 g + a = 42
Final Answer The system of equations that can be used to determine the number of goals and assists the player has is:
g + a = 24 2 g + a = 42
This corresponds to the second option provided in the question.
Examples
Consider a scenario where a company tracks employee performance based on two metrics: completed projects and client interactions. Each completed project earns an employee 2 points, and each client interaction earns 1 point. If an employee has a total of 24 activities (projects and interactions) and accumulates 42 points, this system of equations helps determine the exact number of projects completed and client interactions handled. This approach can be used to optimize performance metrics and allocate resources effectively.
