Question

Jim has a yard sign measuring 45 centimeters by 60 centimeters for his mayoral campaign. He wants to use the same image for a sticker. Jim reduces the image by a scale factor of 15
, and to print the sticker, he reduces the second image by a scale factor of 13.

Answer 1

Let's first analyze the dimensions of the yard sign and how they change when scaled down for the sticker.

1. **Original Yard Sign Dimensions:**
- Width = 45 cm
- Height = 60 cm

2. **Scaling the Image by a Scale Factor of 15:**
To find the dimensions of the first reduced image, we divide each dimension by 15.

- New Width = \( \frac{45 \text{ cm}}{15} = 3 \text{ cm} \)
- New Height = \( \frac{60 \text{ cm}}{15} = 4 \text{ cm} \)

So, the dimensions of the image after the first reduction are:
- Width = 3 cm
- Height = 4 cm

3. **Further Reducing the Image by a Scale Factor of 13:**
Now, we'll take the dimensions after the first reduction (3 cm by 4 cm) and reduce them again by dividing each dimension by 13.

- Final Width = \( \frac{3 \text{ cm}}{13} \approx 0.2308 \text{ cm} \)
- Final Height = \( \frac{4 \text{ cm}}{13} \approx 0.3077 \text{ cm} \)

Thus, the final dimensions of the sticker image, after being scaled down from the yard sign in two steps, are approximately:
- Width = 0.2308 cm
- Height = 0.3077 cm

In conclusion, the final dimensions of the sticker are:
- Width ≈ 0.23 cm
- Height ≈ 0.31 cm