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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.

1 answer

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