Final answer:
To find Jack's original weekly allowance, denote it as A. The equation A/2 + $6.20 = $13.70 is used to represent Jack spending half his allowance plus earnings from cleaning the oven to equal his ending amount. Solving this equation reveals that Jack's weekly allowance was $15.00.
Step-by-step explanation:
The question deals with solving a two-step algebra problem. Jack spent half of his weekly allowance on movies and then gained an additional $6.20 by cleaning the oven. He ended up with $13.70. To find Jack's original weekly allowance, let's denote it as A. When Jack spends half of his allowance, he has A/2 left. Adding the earned $6.20 from cleaning the oven to A/2 gives Jack a total of $13.70:
A/2 + $6.20 = $13.70
Now, we need to solve for A. Subtract $6.20 from both sides of the equation:
A/2 = $13.70 - $6.20
A/2 = $7.50
Finally, multiply both sides by 2 to find Jack's original allowance (A):
A = $7.50 × 2
A = $15.00
Therefore, Jack's weekly allowance was $15.00 before he went to the movies.