Question

Mrs Smith goes on a rail journey with a friend. The friend has a rail card which gives her 20% off the cost of her ticket. Mrs Smith pays full price. The cost of both tickets together is £71.19. How much is Mrs Smith’s ticket?

Answer 1

£39.55 is the price of Mr. Smith's ticket

Explanation:

Let x be the cost of a full ticket (in £).

Mr. Smith's ticket costs x (full price)

Friend's ticket is (1 - 0.20)x or 0.8x

The cost for both tickets is

x + 0.8x or 1.8x

We are now told that both tickets costs a total of £71.19, so we can write:

1.8x = £71.19

x = £39.55 The price of Mr. Smith's ticket

CHECK:

Does one full price and one 20% off price tickets cost a total of £71.19?

Full: = £39.55

Reduced: = (1- 0.2)*(£39.55)

Reduced = £31.64 Friend's Ticket

Total = £71.19 YES