Question

A torch and battery cost £2.50 altogether.The torch costs £1.50 more than the battery.

What fraction of the total price is the torch?

Answer 1

80% of the total price is torch.

Explanation:

Let

t=cost of torch

b=cost of battery

A torch and battery cost £2.50 altogether.

t+b=2.5

The torch costs £1.50 more than the battery.

t-b=1.5

Keep in mind:

When equations of the form

a+b = Sum

a-b = Diff

then the solution is immediately

a=(Sum+Difference)/2

b=(Sum-Difference)/2

and apply the rule,

t=(2.5+1.5)/2 = £2

b=(2.5-1.5)/2 = £1

Torch / total

= 2/2.5

= 80%

Answer 2

4/5

Explanation:

t + b = 2.50

t = b+1.50

Substitute

b+1.50+ b = 2.50

Combine like terms

2b + 1.50=2.50

2b =1

b = .5

t = b+ 1.5

t = .5+ 1.5

t = 2

The fraction of the total price

t/2.50

2/2.50

20/25

4/5