https://file.aiquickdraw.com/mathbot/file/1730331793733mdmv31ix.jpg

To solve these problems, we need to maintain the same aspect ratio (height-to-width ratio) as the original photo, which is \( \frac{4}{6} = \frac{2}{3} \).

Let's solve each part:

### Part (a)
The original photo is 6 inches wide, and Silvia wants to enlarge it to 48 inches wide. Since the height and width should stay proportional, we can set up a proportion:

\[
\frac{4}{6} = \frac{\text{new height}}{48}
\]

Solving for the new height:
\[
\text{new height} = \frac{4 \times 48}{6} = 32 \text{ inches}
\]

So, the enlarged photo will be **32 inches tall**.

### Part (b)
For the wallet-sized photo, Silvia wants the height to be 1.5 inches. Using the same aspect ratio, we set up the proportion:

\[
\frac{4}{6} = \frac{1.5}{\text{new width}}
\]

Solving for the new width:
\[
\text{new width} = \frac{1.5 \times 6}{4} = 2.25 \text{ inches}
\]

So, the wallet-sized photo will be **2.25 inches wide**.

---

Would you like further clarification on any part of this solution?

### Related Questions
1. If Silvia wanted a photo 60 inches wide, how tall would it be?
2. What would the height be if Silvia wanted a 24-inch wide photo?
3. If she reduces the photo width to 3 inches, what would the new height be?
4. How would you set up a proportion for a photo that needs to fit a specific frame size?
5. Can Silvia maintain the aspect ratio if she only changes the width or height independently?

### Tip
Always maintain the aspect ratio by setting up proportions. This keeps images from becoming distorted when resizing.

Silvia has a picture from her trip to the Grand Canyon. The photo is 4 inches tall by 6 inches wide.

  a. She would like to make a larger photo for her wall that is as big as possible. The widest the enlarged photo can be is 48 inches. How tall will the enlarged photo be?

  b. Silvia also wants a wallet-sized photo to carry around and show her friends. She wants it 1.5 inches tall. How wide will it be?

Learn how to calculate the dimensions of an enlarged photo and a wallet-sized photo using proportions. This problem involves setting up ratios to maintain the aspect ratio of the original 4x6 inch photo. Suitable for students in Grades 6-8.

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