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### 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.