Question

mr. lambert’s language arts class participated in a read-and-write challenge during april. for each of the first 10 days, noah read for x minutes and wrote in his journal for 15 minutes. for each of the last 20 days, noah read for x minutes and wrote in his journal for 30 minutes. pick all the expressions that represent how long noah spent reading and writing during the challenge. 10(x + 15) + 20(x + 30) 10x + 150 + 20x + 600 30x + 750 30(x + 15) + 30(x + 30)

Explanation:

First, we calculate the total time Noah spent reading and writing for the first 10 days and the last 20 days.

Step 1: Calculate time for first 10 days

For the first 10 days, Noah read for \( x \) minutes and wrote for 15 minutes each day. So the total time per day is \( x + 15 \) minutes, and for 10 days, it's \( 10(x + 15) \) minutes.

Step 2: Calculate time for last 20 days

For the last 20 days, Noah read for \( x \) minutes and wrote for 30 minutes each day. So the total time per day is \( x + 30 \) minutes, and for 20 days, it's \( 20(x + 30) \) minutes.

Step 3: Calculate total time

The total time is the sum of the time for the first 10 days and the last 20 days:
\[

$$\begin{align*} \text{Total time} &= 10(x + 15) + 20(x + 30) \\ &= 10x + 150 + 20x + 600 \\ &= 30x + 750 \end{align*}$$

\]
We can also factor it as \( 30(x + 25) \), but let's check the given expressions:

• \( 10(x + 15) + 20(x + 30) \): This is the direct calculation of total time, so it's valid.
• \( 10x + 150 + 20x + 600 \): Simplifying the above expression gives this, so it's valid.
• \( 30x + 750 \): Combining like terms from the simplified expression gives this, so it's valid.
• \( 30(x + 15) + 30(x + 30) \): Let's expand this: \( 30x + 450 + 30x + 900 = 60x + 1350 \), which is not equal to the total time, so it's invalid.

Answer:

The expressions that represent the total time are \( 10(x + 15) + 20(x + 30) \), \( 10x + 150 + 20x + 600 \), and \( 30x + 750 \).