### 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.**

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