Question

Jack went to the cash point. He drew out the same amount of money as he had in his pocket. He then spent £40 on CDs.
Jack went back to the cash point.
He drew out the same amount of money as he had in his pocket.
He then spent a further £40 on CDs. Jack did this a third time.
He then had no money left. How much money did he have with him to start?

Answer 1

Suppose that Jack had with him to start £x.

Jack went to the cash point. He drew out the same amount of money as he had in his pocket.

$$£x+£x=£(2x)$$

He then spent £40 on CDs

$$£(2x-40)$$

Jack went back to the cash point. He drew out the same amount of money as he had in his pocket.

$$2£(2x-40)=£(4x-80)$$

He then spent a further £40 on CDs

$$£(4x-80-40)=£(4x-120)$$

Jack went back to the cash point. He drew out the same amount of money as he had in his pocket.

$$2£(4x-120)=£(8x-240)$$

He then spent a further £40 on CDs

$$£(8x-240-40)=£(8x-280)$$

He then had no money left

$$£(8x-280)=£(0)$$

$$8x-280=0$$

$$8x=280$$

$$x=35$$

Jack had with him to start £35.