Let's work through the information step by step. We know that James spent half of his weekly allowance on clothes and ended up with $15. If we let x represent his weekly allowance, then he spent x/2 on clothes.
After that, his parents let him clean the oven for $8. So the total amount he earned would be x/2 + $8.
Since James ended up with $15 in total, we can set up the equation:
x/2 + $8 = $15
To solve for x, we can subtract $8 from both sides of the equation:
x/2 = $15 - $8
x/2 = $7
Multiplying both sides of the equation by 2, we get:
x = $14
Therefore, James's weekly allowance is $14.