# Three part ratios

Just as two part ratio means

x to every y

read three part ratio in the same way

x:y:z

x to every y to every z

This can be shown as x:y:z or

x/y/z or

x to y to z

Example 1

One of the most famous examples is in mixing concrete

1 cement: 2 sand: 3 Aggregate (stone)

This means mix

1 part cement to every 2 part sand to every 3 parts aggregate.

Example 2

Jane has 2 apples Mary has 4 apples and Elaine has 3 apples. What is the ratio of the amount of apples Jane has to the amount Mary has and to the amount Elaine has?

The answer is 2 to every 4 to every 3 or

2:4:3 or more simply

1:2:1.5

Example 3

The ratio of red to blue to green balls is 3:4:5 If there are actually 28 blue balls how many balls are there in all?

3:4:5

Means 3 red to every 4 blue to every 5 green is the rato.

If there are 28 blue balls that means there are

28/4=7

there are 7 times as many blue balls than the ratio, so there must be 7 times as many red and green balls too.

Therefore

3times7 to every 4times7 to every 5times7

21 to every 28 to every 35

This means there are

 21 +28 +35 84

The total number of balls is 84

Example 4

A lottery win of 90,000 has to be divided in the ratio of 2:3:4 How is the money split?

Answer this by finding the total number of the parts of the ratio

Remember 2:3:4

means 2 to every 3 to every 4

 The total number of parts = 2 +3 +4 9

The total number of parts is 9

9 parts =90,000

1 part =x

(use the same system as in how to do percentages in Mammoth memory) and you know this becomes:

9/1=(90,000)/x

Therefore x=(90,000)/9times1

x=10,000

Therefore 1 part =£10,000

Therefore the money should be divided in the ratio of

2:3:4

2times£10,000:3times£10,000:4times£10,000

£20,000         :    £30,000    :         £40,000

This is how the money should be divided.

Double check by adding these up

 20,000 +30,000 +40,000 90,000

So the amounts are correct.