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### Rule of three direct proportion

The rule of three is a method to solve proportions. If we have three numbers: a, b, c, such that, (a / b = c / x), (i.e., a: b :: c: x) we can calculate the unknown value (x).
We have, by the expression: (a : b :: c : x), that the product of the means is equal to the product of the extremes, using the cross-multiplication method, where:
a*x = b*c.
Direct Proportion
If, a change in the amount causes a change in the unknown amount, at the same proportion, the amounts are in direct proportion.
Example 1
If, 4 kg of a product have a cost of \$36.00, how much would the cost of 18kg? Problem formulation:
4 kg -   cost \$36.00
18 kg -   cost x
Solution:
By applying the cross products rule on the expression below:
Mathematical Formulation
4 / 18 = 36 / x;
So, we have:
x = (18 * 36) / 4 = 162;
x = \$162.00
As seen, the increased quantity, resulting in an increased cost.
Example 2
To fill a 1,000-gallon tank takes two hours. What is the necessary time to fill the tank with 9500 gallons?
Solution:
1000/ 9500 = 2 / x;
x = (9500 * 2) / 1000 = 19;
x = 19 hours.
How to calculate the Rule of three - direct proportion.