# Composite proportionality

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
• 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) candies and (number of) hours . The unknown variable is hours .

Relationship between the variables (with the unknown variable):

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

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.