# Problems from Compound rule of three

In July, a family of $$4$$ people spends $$10$$ days in a hotel on the beach for $$2.500$$ €. How much it will be for a group of $$6$$ persons to spend the second two weeks of July in the same hotel?

See development and solution

### Development:

The first step to solve the exercise is to outline the compound rule of three and to analyze the relation of the unknown with the other two parameters:

$$\begin{eqnarray} & d & & d & \\\\ 4\ \mbox{people} & \rightarrow & 10 \ \mbox{days} & \rightarrow & 2500 \ \mbox{€} \\\\ 6\ \mbox{people} & \rightarrow & 15 \ \mbox{days} & \rightarrow & x \ \mbox{€} \\\\ & d & & d & \end{eqnarray}$$

So that the relation between the amount of euros and the number of persons is direct since: the more people there are, the more money it will cost. In the same way, the relation between the days and the price is also direct since the more days of accommodation the more expensive it will be.

As soon as the analysis is done, the transformation in fractions is immediate:

$$\dfrac{4}{6}\cdot\dfrac{10}{15}=\dfrac{2500}{x} \Rightarrow \dfrac{40}{90}=\dfrac{2500}{x} \Rightarrow 40x=90\cdot2500 \Rightarrow$$ $$40x=225.000 \Rightarrow x=\dfrac{225.000}{40}=5625$$€

### Solution:

$$5625$$€

Hide solution and development