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# 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?

C. COMPOUND RULE OF THREE

We say that we have compound proportionality when we have more than 2 magnitudes.

1. A farmer has needed 294 kilos of food to feed 15 cows for a week. How many kilos of food does the farmer need to feed 10 cows for 30 days?

- We have to identify the magnitudes

- We have to order magnitudes and data.

- We have  to identify the proportionality relationship between the magnitude to the unknown datum and the others.

NOTE: It is useful to put the magnitude with the unknown datum in the last position.

2. A team of workers will build a wall of 400 m2 in 15 days if they work 8 hours everyday. How long will they take if the wall has 600 m2 and they work 10 hours everyday?

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?

3.- If 5 trucks transport 120 tons of goods in 2 days: what goods quantity will 7 trucks transport in 3 days?

4.- It takes 15 days for a team of 10 workers working 8 hours a day to finish an order. How many people with part time jobs (half the day) will be needed to do the same work in 10 days?

Solutions: 1) 12,50 €; 2) 18 hours; 3) 252 tons; 4) 30 persons