### Rule of three inverse proportion

The rule of three is a method to solve proportions.
If you have three numbers: a, b, c, such that, ( a / b = c / x), or a: b :: c: x )
you can calculate the unknown value (x).

We have, by the expression: (a : b :: c : x), where the product of the means is equal to the product of the extremes, using the cross products rule, where:

b * c = a * x.

**Inverse Proportion**

When, the increase of a quantity , causes a decrease in the other one, or by the contrary, a decreasing causing the increase in the other one, this is, an
inverse proportion , or the two quantities are inversely proportional.

The expression: a / b = c / x (direct proportion) is now:** (b / a = c / x)**, for the inverse proportion, because, we change the terms of the first
equality, where the numerator becomes the denominator and vice versa.

Example:

If two workers take 16 days to build 100m of fence, how many days will be spent using four workers?

Problem formulation.

2 workers = 16 days

4 workers = x days

a / b = c / x )

Since the ratio is inversely proportional, we change the terms of the first equality.

Mathematical Formulation:

b / a = c / x)

x =( a * c) / b )

And now, replacing, the letters, we have:

X = (2 * 16) / 4) = 8 days.

So, as seen above, increasing workers quantities, resulting in decreased days.

How to calculate the **Rule of three - inverse proportion.**

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