Let x equal his allowance.
He earns $7 for washing the family car.
His total intake is x + 7
He spent half of his allowance going to the movies.
This means he spent 1/2 * x going to the movies.
He has $15 left.
You get:
x + 7 - 1/2 * x = 15.
Combine like terms to get 1/2 * x + 7 = 15.
Subtract 7 from both sides of the equation to get 1/2 * x = 15 - 7
Simply to get 1/2 * x = 8
Multiply both sides of this equation by 2 to get x = 8 * 2.
Simplify to get x = 16
His allowance must have been $16
He washes the family car and earns $7.
He now has $23.
He spends half of his allowance, which is $11.50 on the movies which means he spent $5.75 on the movies.
He now has $23 - $5.75 = $17.25.
His allowance had to be $16.