## 275. Math Puzzle $4 / 88$

A photography enthusiast enlarges a hiking map with dimensions $20 \mathrm{~cm}$ x $35 \mathrm{~cm}$ and a scale of 1:10000 to a format of $50 \mathrm{~cm}$ x 87.5 cm, maintaining the scale.

What scale does the newly created hiking map have?
When the dimensions of the hiking map are scaled up proportionally, its scale (M) is reduced.

It holds that: $\frac{50 \mathrm{~cm}}{20 \mathrm{~cm}}=\frac{87.5 \mathrm{~cm}}{35 \mathrm{~cm}}=2.5$

$$
M_{2}=\frac{M_{1}}{2.5}=\frac{10000}{2.5}=4000
$$

The newly created hiking map has a scale of 1:4000.