Question: A garden centre has 75 trees that are small, medium or large.
For every small tree there are 7 medium trees.
For every large tree there are 3 small trees.
Calculate the number of small trees in the garden centre.
1. **State the problem:** We have a total of 75 trees divided into small, medium, and large categories.
2. **Define variables:** Let $S$ be the number of small trees, $M$ the number of medium trees, and $L$ the number of large trees.
3. **Write the relationships given:**
- For every small tree, there are 7 medium trees: $$M = 7S$$
- For every large tree, there are 3 small trees: $$L = \frac{S}{3}$$
4. **Write the total trees equation:**
$$S + M + L = 75$$
5. **Substitute $M$ and $L$ in terms of $S$:**
$$S + 7S + \frac{S}{3} = 75$$
6. **Combine like terms:**
$$8S + \frac{S}{3} = 75$$
7. **Find common denominator and add:**
$$\frac{24S}{3} + \frac{S}{3} = 75$$
$$\frac{25S}{3} = 75$$
8. **Multiply both sides by 3:**
$$25S = 225$$
9. **Divide both sides by 25:**
$$S = \frac{225}{25}$$
$$S = 9$$
**Final answer:** There are **9 small trees** in the garden centre.