# 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

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