# Three simple rule

Simple three rule is a practical process for solving problems involving four values ​​of which we know three of them. We must therefore determine a value from the three already known.

## Steps used in a simple three rule

1º) Construct a table by grouping the quantities of the same species into columns and keeping in line with the quantities of different species in correspondence.

2º) Identify whether the quantities are directly or inversely proportional.

3º) Assemble the ratio and solve the equation.

## Examples

1) With a solar absorption area of ​​1.2m2, a solar-powered motorboat can produce 400 watts per hour of power. Increasing this area to 1.5m2, what will be the energy produced?

Solution: setting up the table:

 Area (m2) Energy (Wh) 1,2 400 1,5 x

Relationship Type Identification:

Initially we put a down arrow on the column containing x (2nd column). Notice that, increasing absorption area, solar energy increases. As the words correspond (increasing - increasing), we can say that the magnitudes are directly proportional.

So we put another arrow in the same direction (down) in the 1st column. Riding the ratio and solving the equation we have:

Therefore, the energy produced will be 500 watts per hour.

2) A train, moving at an average speed of 400 km / h, makes a certain journey in 3 hours. How long would that same route be if the speed used was 480km / h?

Solution: setting up the table:

 Speed ​​(Km / h) Time (h) 400 3 480 x

Relationship Type Identification:

Initially we put a down arrow on the column containing x (2nd column). Notice that, increasing the speed, the travel time decreases. Since the words are contrary (increasing - decreasing), we can say that the quantities are inversely proportional.

So we put another arrow upwards in the 1st column. Riding the ratio and solving the equation we have:

Therefore, the time of this route would be 2.5 hours or 2 hours and 30 minutes.

3) Bianca bought 3 t-shirts and paid $120.00. How much would she pay if she bought 5 shirts of the same type and price? Solution: setting up the table:  T-Shirts Price (R$) 3 120 5 x

Notice that, increasing the number of t-shirts, the price increases. As the words correspond (increasing - increasing), we can say that the magnitudes are directly proportional.

Riding the ratio and solving the equation we have:

Soon, Bianca would pay \$ 200 by 5 shirts.

4) A team of workers, working 8 hours a day, performed a certain work in 20 days. If the number of hours of service is reduced to 5 hours per day, when will this team do the same work?

Solution: setting up the table:

 Hours per day Deadline (days) 8 20 5 x

Notice that, decreasing the number of hours worked per day, the deadline to finish increases. Since the words are contrary (decreasing - increasing), we can say that the quantities are inversely proportional.

Riding the ratio and solving the equation we have:

Next: Composite Three Rule