# Compound Three Rule

The compound three rule is used for problems with more than two quantities, directly or inversely proportional.

## Examples

1) In 8 hours, 20 trucks unload 160m3 of sand. In 5 hours, how many trucks will need to unload 125m3?

Solution: setting up the table, placing in each column the quantities of the same species and, in each row, the quantities of different species that correspond:

 Hours Trucks Volume 8 20 160 5 x 125

Identification of relationship types:Initially we put a down arrow on the column containing x (2nd column). Next, we must compare each quantity with that where x is. Notice that, increasing the number of working hours we can decrease The number of trucks. So the relationship is inversely proportional (up arrow in 1st column).

Increasing the volume of sand we should increase The number of trucks. So the relationship is directly proportional (down arrow in 3rd column). We must equate the ratio containing the term x with the product of the other ratios according to the direction of the arrows.

Assembling the ratio and solving the equation, we have:  Therefore, it will be necessary 25 trucks.

2) In a toy factory, 8 men assemble 20 strollers in 5 days. How many carts will be assembled by 4 men in 16 days?

Solution: setting up the table:

 Men Carts Days 8 20 5 4 x 16

Notice that, increasing the number of men, the production of strollers increases. So the relationship is directly proportional (we don't need to reverse the reason).

Increasing The number of days, the production of carts increases. So the relationship is also directly proportional (we don't need to reverse the reason). We must equate the ratio containing the term x with the product of the other ratios.

Assembling the ratio and solving the equation, we have: Soon they will be assembled 32 carts.

3) Two masons take 9 days to build a 2m high wall. Working 3 masons and increasing the height to 4m, how long will it take to complete this wall?

Initially we put a down arrow on the column containing x. Then put matching arrows for the quantities directly proportional with the unknown and discordant to the inversely proportionalas shown below: Assembling the ratio and solving the equation, we have: Therefore, to complete the wall will require 12 days.

## Complementary Exercises

Now it's your turn to try. Practice trying to do these exercises:

1) Three taps fill a pool in 10 hours. How many hours will it take 10 taps to fill 2 pools?