Question

A torch and a battery cost £2.50 altogether. The torch costs £2.00 more than the battery.

What fraction of the total price is the battery? Give your answer in it's simplest form

Answer 1

`(1)/(10)`

Explanation:

Let
`t` represent the cost of the torch and
`b` represent the cost of the battery.

The torch and a battery cost £2.50 altogether.

`\Rightarrow t+b=2.50`

The torch costs £2.00 more than the battery.

`\Rightarrow t=b+2.00`

We substitute the second equation into the first equation to get;

`\Rightarrow b+2.00+b=2.50`

`\Rightarrow 2b=2.50-2.00`

£2.50

`\Rightarrow 2b=0.50`

`\Rightarrow b=0.25`

The price of the battery is £0.25

We express this as a fraction of the total cost which is £2.50 to get;

`(0.25)/(2.5)=(1)/(10)`