Question

the photo shows a small coin. the scale from the actual coin to the photo is 8 mm to 2 cm. in the photo, the distance across the coin is 3.25 cm. what is the distance across the actual coin? show your work.

Explanation:

Step1: Convert units

Since \(1\ cm = 10\ mm\), then \(2\ cm=2\times10 = 20\ mm\).

Step2: Set up proportion

Let \(x\) be the actual distance across the coin (in mm). The scale is \(\frac{\text{actual}}{\text{photo}}=\frac{8}{20}\). We know the photo - distance is \(3.25\ cm = 3.25\times10=32.5\ mm\). Using the proportion \(\frac{8}{20}=\frac{x}{32.5}\).

Step3: Solve the proportion

Cross - multiply: \(20x=8\times32.5\). So \(20x = 260\). Then \(x=\frac{260}{20}=13\) mm.

Answer:

The distance across the actual coin is \(13\) mm.