# 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?

To answer this understand that

`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.