Angela earns a weekly allowance at the start of each week. She started the week with just her weekly allowance. Then, she spent half of her weekly allowance at the movies. To earn more money, her parents let her clean the windows in the house for $5. What is her weekly allowance if she ended the week with $8? Solve using arithmetic or algebra, and explain your steps.

Answer 1

Let's represent Angela's weekly allowance as x.
She spent half of her weekly allowance at the movies, so she spent (1/2)x dollars.
After spending (1/2)x dollars, she had x - (1/2)x = (1/2)x dollars left.
Then, she earned $5 by cleaning the windows.
Adding the $5 to her remaining allowance, we have (1/2)x + $5 = x - (1/2)x + $5.
Simplifying the equation, we have (1/2)x + $5 = (3/2)x + $5.
Subtracting (1/2)x from both sides, we have $5 = (3/2)x + $5 - (1/2)x.
Simplifying further, we have $5 = x + $5.
Subtracting $5 from both sides, we have 0 = x.
Therefore, her weekly allowance is $0.