Question

Pam takes a picture of a painting to use the image for a postcard. The painting is 16 inches by 40 inches. She reduces the image by a scale factor of 14
to view the image on her computer. Pam further reduces the image by a scale factor of 12
to match the dimensions of a postcard.



What are the dimensions of the postcard? Write the smaller dimension first and the larger dimension second

Answer 1

To find the dimensions of the postcard after the reductions, we'll follow these steps:

1. **Original dimensions of the painting**: 16 inches by 40 inches.

2. **First reduction by a scale factor of 14**:
- Smaller dimension: \( \frac{16}{14} = \frac{8}{7} \) inches
- Larger dimension: \( \frac{40}{14} = \frac{20}{7} \) inches

3. **Second reduction by a scale factor of 12**:
- Smaller dimension: \( \frac{8/7}{12} = \frac{8}{84} = \frac{2}{21} \) inches
- Larger dimension: \( \frac{20/7}{12} = \frac{20}{84} = \frac{5}{21} \) inches

Now, we have:
- Smaller dimension: \( \frac{2}{21} \) inches
- Larger dimension: \( \frac{5}{21} \) inches

To express these dimensions without fractions, we can multiply both dimensions by 21:
- Smaller dimension: \( 2 \) inches
- Larger dimension: \( 5 \) inches

Thus, the dimensions of the postcard, with the smaller dimension first, are **2 inches by 5 inches**.