Fred ended with $11. So, subtract $9 from washing the car.
$11 - $9 = $2
$2 Is the amount of weekly allowance Fred <em>hasn't</em><em> </em>spent yet. However, at the beginning of the week, Fred used half his allowance. This means $2 was what was left. So,
$2 × 2 = $4
meaning Fred had $4 in allowance at the beginning of the week.
