Can someone help me solve this brain teaser?

Question

You send an invoice to a customer for goods he has purchased from you, however, when he sends payment he makes a mistake and transposes the pounds and pence. You do not realise this, and when you cash the cheque you spend £9.52. You then discover that you now have exactly twice as much cash as the amount of the invoice. What was the total of this invoice?

Answer 1

I'm usually good at these but I'm having trouble actually understanding the question!

The bit about spending £9.52 when you cash a cheque. (?)

Answer 2

Invoice = 100 x + y

Payment = 100 y + x

100 y + x - 952 = 2 (100 x + y)

100y + x - 952 = 200x + 2y

98y - 199x = 952

y = (952 + 199x)/98

Solution in integers between 1 and 100:

x = 42 y = 95

Invoice was 42.95

Payment was 95.42

95.42 - 9.52 = 85.90 = 2 * 42.95

.

Answer 3

I could understand it if you translated it into money, but sorry I don't know that currency...