https://file.aiquickdraw.com/mathbot/file/17302492658318sg7xmzh.jpg

Let's analyze and solve the problem in the image.

### Problem Breakdown

1. The table shows the relationship between **Time (minutes)** and **Pages Read**. Given values are:
   - **50 minutes** corresponds to **60 pages**.
   - **80 minutes** corresponds to **96 pages**.

2. We need to:
   - **(a)** Fill in the red boxes by determining the multiplicative relationship.
   - **(b)** Find out how many pages Thomas can read in **30 minutes**.

### Solution

#### Part (a): Filling in the Multiplicative Relationship

1. To find the **pages per minute** rate:
   - Since Thomas reads **60 pages in 50 minutes**, we calculate the rate as:
     \[
     \text{Rate} = \frac{60}{50} = 1.2 \text{ pages per minute}
     \]

2. Using this rate, let’s fill in the red boxes:
   - **First row**: \(50 \times 1.2 = 60\)
     - So, the multiplier in the first row is \(1.2\).
   - **Second row**: We know 80 minutes corresponds to 96 pages. Dividing to check the rate:
     \[
     96 \div 1.2 = 80
     \]
     - So, the divisor in the second row is \(1.2\).

Thus, the completed table should show:
   - **Multiplier** for the first row is \(1.2\).
   - **Divisor** for the second row is \(1.2\).

#### Part (b): Calculating Pages in 30 Minutes

1. Using the rate of **1.2 pages per minute**, the number of pages Thomas can read in 30 minutes is:
   \[
   30 \times 1.2 = 36 \text{ pages}
   \]

### Answers

- **(a)** Fill in the table with **1.2** as the multiplier (for 50 to 60 pages) and divisor (for 80 to 96 pages).
- **(b)** Thomas can read **36 pages in 30 minutes**.

Would you like further details or explanations on any part?

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#### Related Questions for Practice:

1. If Thomas read for 100 minutes, how many pages would he read?
2. How many minutes would it take Thomas to read 72 pages?
3. If Thomas’s reading rate increased to 1.5 pages per minute, how many pages could he read in 50 minutes?
4. What would Thomas’s reading time be if he read 120 pages at the rate of 1.2 pages per minute?
5. How would the answers change if Thomas read only 0.8 pages per minute?

#### Tip:
When dealing with rate problems, always start by finding the unit rate, as it simplifies calculations for other amounts.

Thomas can read about 60 pages of his book in 50 minutes. The table shows how many pages he can read in different amounts of time.

Time (minutes) | Pages Read
50             | 60
80             | 96

Fill in the table to show the multiplicative relationship and determine how many pages Thomas can read in 30 minutes.

Learn how to determine the number of pages Thomas can read in a given time by filling in the multiplicative relationships. This problem explores ratios and proportions, helping students understand time-based calculations.

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