Three variables intervene in **compound proportionality** problems , one of them being the **unknown variable** . The relationship between the variables with the unknown variable can be a simple **direct** or **inverse **proportionality . They are solved by applying a compound **rule of three** .

## Summary

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- 1 Example
- 1 Resolution
- 2 See also
- 3 Sources.

# Example

**Problem:** If 6 children eat 160 candies in 2 hours, how many hours does it take 3 children to eat 120 candies?

## Resolution

**Variables:** The variables of the problem are: *(number of) children* ,

*(number of)*and

**candies***(number of)*. The unknown variable is

**hours***hours*.

**Relationship between the variables (with the unknown variable):**

: the more children there are, the fewer hours it takes to eat the candy. It is an inverse proportionality.*Children-hours*: the more candy there is, the more hours it takes to eat them. It is a direct proportionality.*Candy-hours*

**Table with the data:** we write a table with the data, leaving the variable unknown in the third column and indicate with arrows if it is a direct (D) or inverse (I) proportionality.

**Compound rule of three:** We write the two columns on the left as two fractions that are multiplied and equaled with the column on the right:

**Important:**

- If it is direct proportionality, we write the first row divided by the second.
- If it is an inverse proportionality, we write the second row divided by the first row.

**We calculate the unknown** factor by solving for the *x* :

Therefore, it takes 3 children 3 hours to eat 120 candies.