Question: The heights of three Russian dolls are in the ratio 7 : 12 : 17
Write this ratio in the form 1 : m : n
Give m and n as decimals to 2 d.p.
1. **State the problem:** We are given the ratio of the heights of three Russian dolls as $$7 : 12 : 17$$.
2. **Goal:** Write this ratio in the form $$1 : m : n$$ where $$m$$ and $$n$$ are decimals rounded to 2 decimal places.
3. **Formula and explanation:** To convert the ratio $$7 : 12 : 17$$ to the form $$1 : m : n$$, divide each term by the first term (7).
4. **Calculate $$m$$:**
$$m = \frac{12}{7}$$
5. **Calculate $$n$$:**
$$n = \frac{17}{7}$$
6. **Perform the division:**
$$m = 1.7142857... \approx 1.71$$
$$n = 2.4285714... \approx 2.43$$
7. **Final ratio:**
$$1 : 1.71 : 2.43$$
**Answer:** $$m = 1.71$$ and $$n = 2.43$$.