Let's define the variables first:

• Let $S$ be the number of small trees.
• Let $M$ be the number of medium trees.
• Let $L$ be the number of large trees.

We know that:

1. $S + M + L = 99$ (there are 99 trees in total).
2. $M = 7S$ (for every small tree, there are 7 medium trees).
3. $S = 4L$ (for every large tree, there are 4 small trees).

Step-by-step Solution:

1. Using equation (2), substitute $M = 7S$ into equation (1): $S + 7S + L = 99$ Simplify this: $8S + L = 99$

2. Now use equation (3), $S = 4L$, to express $L$ in terms of $S$: $L = \frac{S}{4}$

3. Substitute $L = \frac{S}{4}$ into the equation $8S + L = 99$: $8S + \frac{S}{4} = 99$

4. To eliminate the fraction, multiply the entire equation by 4: $32S + S = 396$ Simplify: $33S = 396$

5. Solve for $S$: $S = \frac{396}{33} = 12$

Thus, the number of small trees in the garden centre is 12.

Additional calculations:

• Number of medium trees: $M = 7S = 7 \times 12 = 84$.
• Number of large trees: $L = \frac{S}{4} = \frac{12}{4} = 3$.

This checks out, as $12 + 84 + 3 = 99$.

Would you like more details, or do you have any questions?

Here are some related questions:

1. How many medium trees are there in the garden center?
2. If the total number of trees increased to 150, how would that affect the number of small trees?
3. How can the ratio of small to large trees be expressed in simplest terms?
4. What percentage of the total trees are large trees?
5. What would happen if the ratio between medium and small trees changed to 6:1?

Tip: Breaking a problem into steps and substituting values can simplify complex equations.