Given that Sarah spent half of her weekly allowance.
She earns $4.70 for washing dogs.
The final amount is $ 13.50.
Let x be the weekly allowance.
She spent half of her allowance so she has half of the allowance.
She earns $ 4.70, add this to her half of the allowance.
This is equal to 13.50.
Subtracting 4.70 from both sides, we get
Multiplying 2 on both sides, we get
Hence Sarah's weekly allowance is $ 17.60.