$C=290+155 h$ $\newline$ A team of painters is hired to paint the exterior of a museum. The total cost, $C$ , in dollars, incurred by the museum for $h$ hours of painting is given by the equation. What is the best interpretation of $155$ in the equation? $\newline$ Choose $1$ answer: $\newline$ A The total cost can be at most $\$ 155$ . $\newline$ B It takes the team $155$ hours to paint the exterior. $\newline$ (C) Each additional hour of painting the exterior costs $\$ 155$ . $\newline$ (D) $\$ 155$ is the base cost regardless of how many hours it takes to paint the exterior.

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Interpret parts of quadratic expressions: word problems

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C=290+155 h

\newline

A team of painters is hired to paint the exterior of a museum. The total cost,

C

, in dollars, incurred by the museum for

h

hours of painting is given by the equation. What is the best interpretation of

155

in the equation?

\newline

Choose

1

answer:

\newline

A The total cost can be at most

\$ 155

\newline

B It takes the team

155

hours to paint the exterior.

\newline

\$ 155

\newline

(D)

\$ 155

is the base cost regardless of how many hours it takes to paint the exterior.

Understand Equation Structure: To interpret the meaning of $155$ in the equation, we need to understand the structure of the equation $C=290+155h$ . This is a linear equation where $C$ represents the total cost, $h$ represents the number of hours, and the numbers $290$ and $155$ are constants.
Interpret Constant Values: The constant $290$ is the initial value when $h$ (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 $155$ is multiplied by the variable $h$ (hours). This indicates that for every hour of work, the cost increases by $155$ dollars. Therefore, $155$ represents the cost per hour of painting.
Evaluate Given Options: The constant $155$ is multiplied by the variable $h$ (hours). This indicates that for every hour of work, the cost increases by $155$ dollars. Therefore, $155$ represents the cost per hour of painting.Now, let's evaluate the options given: $\newline$ (A) The total cost can be at most $\$155$ . This is incorrect because $155$ is multiplied by the number of hours, which means it is not a maximum total cost.
Evaluate Given Options: The constant $155$ is multiplied by the variable $h$ (hours). This indicates that for every hour of work, the cost increases by $155$ dollars. Therefore, $155$ represents the cost per hour of painting.Now, let's evaluate the options given: $\newline$ (A) The total cost can be at most $\$155$ . This is incorrect because $155$ is multiplied by the number of hours, which means it is not a maximum total cost.(B) It takes the team $155$ 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 $155$ is multiplied by the variable $h$ (hours). This indicates that for every hour of work, the cost increases by $155$ dollars. Therefore, $155$ represents the cost per hour of painting.Now, let's evaluate the options given: $\newline$ (A) The total cost can be at most $\$155$ . This is incorrect because $155$ is multiplied by the number of hours, which means it is not a maximum total cost.(B) It takes the team $155$ 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 $\$155$ . This is the correct interpretation because the equation shows that for each hour, the cost increases by $155$ dollars.
Evaluate Given Options: The constant $155$ is multiplied by the variable $h$ (hours). This indicates that for every hour of work, the cost increases by $155$ dollars. Therefore, $155$ represents the cost per hour of painting.Now, let's evaluate the options given: $\newline$ (A) The total cost can be at most $\$155$ . This is incorrect because $155$ is multiplied by the number of hours, which means it is not a maximum total cost.(B) It takes the team $155$ 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 $\$155$ . This is the correct interpretation because the equation shows that for each hour, the cost increases by $155$ dollars.(D) $\$155$ 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 $h$ $0$ , not $155$ .