Question

sue and martina are going to a movie. they plan to walk to the theater, watch the movie, and walk home. the walk will take m minutes each way, while the movie lasts 120 minutes.
pick all the expressions that represent how much time their outing will take.
2m + 120
m(2 + 120)
2(m + 120)
m + 120 + m

Explanation:

Step1: Analyze the time components

The total time for the outing includes the time to walk to the theater, the time to watch the movie, and the time to walk home. The walk to the theater takes \( m \) minutes, the movie takes 120 minutes, and the walk home takes \( m \) minutes. So the total time is the sum of these three times: \( m + 120 + m \).

Step2: Simplify the expression

Combining like terms in \( m + 120 + m \), we get \( 2m + 120 \).

Step3: Analyze the other expressions

• For \( m(2 + 120) \), this simplifies to \( m\times122 = 122m \), which is not equal to \( 2m + 120 \) (unless \( m = 0 \), which doesn't make sense in this context). So this expression is incorrect.
• For \( 2(m + 120) \), using the distributive property, this expands to \( 2m + 240 \), which is not equal to \( 2m + 120 \). So this expression is incorrect.
• The correct expressions are \( 2m + 120 \) (from combining like terms in \( m + 120 + m \)) and \( m + 120 + m \) (the original sum of the three time components).

Answer:

The correct expressions are:

• \( 2m + 120 \)
• \( m + 120 + m \)

(Note: The expressions \( m(2 + 120) \) and \( 2(m + 120) \) are incorrect as shown in the analysis above.)