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A team of painters is hired to paint the exterior of a museum. The total cost, , in dollars, incurred by the museum for hours of painting is given by the equation. What is the best interpretation of in the equation?Choose answer:A The total cost can be at most .B It takes the team hours to paint the exterior.(C) Each additional hour of painting the exterior costs .(D) is the base cost regardless of how many hours it takes to paint the exterior.
Full solution
Q. A team of painters is hired to paint the exterior of a museum. The total cost, , in dollars, incurred by the museum for hours of painting is given by the equation. What is the best interpretation of in the equation?Choose answer:A The total cost can be at most .B It takes the team hours to paint the exterior.(C) Each additional hour of painting the exterior costs .(D) is the base cost regardless of how many hours it takes to paint the exterior.
- Understand Equation Structure: To interpret the meaning of in the equation, we need to understand the structure of the equation . This is a linear equation where represents the total cost, represents the number of hours, and the numbers and are constants.
- Interpret Constant Values: The constant is the initial value when (hours) is zero. This suggests that it is a fixed cost that does not depend on the number of hours worked.
- Evaluate Given Options: The constant is multiplied by the variable (hours). This indicates that for every hour of work, the cost increases by dollars. Therefore, represents the cost per hour of painting.
- Evaluate Given Options: The constant is multiplied by the variable (hours). This indicates that for every hour of work, the cost increases by dollars. Therefore, represents the cost per hour of painting.Now, let's evaluate the options given:(A) The total cost can be at most . This is incorrect because is multiplied by the number of hours, which means it is not a maximum total cost.
- Evaluate Given Options: The constant is multiplied by the variable (hours). This indicates that for every hour of work, the cost increases by dollars. Therefore, represents the cost per hour of painting.Now, let's evaluate the options given:(A) The total cost can be at most . This is incorrect because is multiplied by the number of hours, which means it is not a maximum total cost.(B) It takes the team hours to paint the exterior. This is incorrect because the equation does not provide information about the total time required to complete the job; it only gives the cost per hour.
- Evaluate Given Options: The constant is multiplied by the variable (hours). This indicates that for every hour of work, the cost increases by dollars. Therefore, represents the cost per hour of painting.Now, let's evaluate the options given:(A) The total cost can be at most . This is incorrect because is multiplied by the number of hours, which means it is not a maximum total cost.(B) It takes the team hours to paint the exterior. This is incorrect because the equation does not provide information about the total time required to complete the job; it only gives the cost per hour.(C) Each additional hour of painting the exterior costs . This is the correct interpretation because the equation shows that for each hour, the cost increases by dollars.
- Evaluate Given Options: The constant is multiplied by the variable (hours). This indicates that for every hour of work, the cost increases by dollars. Therefore, represents the cost per hour of painting.Now, let's evaluate the options given:(A) The total cost can be at most . This is incorrect because is multiplied by the number of hours, which means it is not a maximum total cost.(B) It takes the team hours to paint the exterior. This is incorrect because the equation does not provide information about the total time required to complete the job; it only gives the cost per hour.(C) Each additional hour of painting the exterior costs . This is the correct interpretation because the equation shows that for each hour, the cost increases by dollars.(D) is the base cost regardless of how many hours it takes to paint the exterior. This is incorrect because the base cost is represented by the constant , not .
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