Answer:
[tex]\frac{1}{10}[/tex]
Step-by-step explanation:
Let [tex]t[/tex] represent the cost of the torch and [tex]b[/tex] represent the cost of the battery.
The torch and a battery cost £2.50 altogether.
[tex]\Rightarrow t+b=2.50[/tex]
The torch costs £2.00 more than the battery.
[tex]\Rightarrow t=b+2.00[/tex]
We substitute the second equation into the first equation to get;
[tex]\Rightarrow b+2.00+b=2.50[/tex]
[tex]\Rightarrow 2b=2.50-2.00[/tex]
£2.50
[tex]\Rightarrow 2b=0.50[/tex]
[tex]\Rightarrow b=0.25[/tex]
The price of the battery is £0.25
We express this as a fraction of the total cost which is £2.50 to get;
[tex]\frac{0.25}{2.5}=\frac{1}{10}[/tex]
