Rules of three

In a problem of proportionality, if we don’t know one datum  in a proportion and we know the other three, we can calculate the unknown datum using cross-product. We call it rule of three.

If the proportionality is direct, we call it direct rule of three, and if it is inverse we call it inverse rule of three.

A. DIRECT RULE OF THREE

1. Adrian finds that in each delivery of 500 bricks there are 20 broken bricks. How many bricks are broken in a delivery of 7500?

2. In a drink of 200 ml of fruit juice there are 140 ml of water. How many litres of water are there in 3 litres of that drink?

B. INVERSE RULE OF THREE

1. A truck that carries 3 tons needs 15 trips to carry a certain amount of sand. How many trips are needed to carry the same amount of sand with another truck that carries 5 tons?

2. Two hydraulic shovels make the trench for a telephone cable in ten days. How long will it take to make the trench with 5 shovels?

Exercises:

1.- I paid 30 euros for 12 chairs. If my friend Charles want 5 chairs as mine. How much does he have to pay?

2.- Three gardeners mow the grass of a park in 12 hours. How long will it take if one of them have to go?

Solutions: 1) 12,50 €; 2) 6 hours