Mammoth Memory

Three part ratios

Just as two part ratio means

`x` to every `y`

read three part ratio in the same way


 `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



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


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

If there are `28` blue balls that means there are


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


`3times7` to every `4times7` to every `5times7`

`21` to every `28` to every `35`

This means there are


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`

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:


Therefore `x=(90,000)/9times1`


Therefore `1` part `=£10,000`

Therefore the money should be divided in the ratio of 



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

This is how the money should be divided.

Double check by adding these up


So the amounts are correct.

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