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.