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.
