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 ALL of your steps!(3 points)

Answer 1

Let's denote Angela's weekly allowance as \( x \).

1. Starting Amount: At the beginning of the week, Angela has her weekly allowance, which is \( x \).

2. Money Spent: She spends half of her weekly allowance at the movies. The amount she spends on the movies is: \[ \frac{1}{2}x \]

3. Amount Left After Movies: After going to the movies, the amount of money Angela has left is: \[ x - \frac{1}{2}x = \frac{1}{2}x \]

4. Earning More Money: Next, Angela cleans the windows to earn $5. Now, her total money after cleaning the windows is: \[ \frac{1}{2}x + 5 \]

5. Ending Amount: We know that Angela ends the week with $8. Therefore, we can set up the following equation: \[ \frac{1}{2}x + 5 = 8 \]

6. Solving the Equation:

   • Start by subtracting 5 from both sides: \[ \frac{1}{2}x = 8 - 5 \] \[ \frac{1}{2}x = 3 \]
   • Next, multiply both sides by 2 to get \( x \): \[ x = 3 \times 2 \] \[ x = 6 \]

7. Conclusion: Angela's weekly allowance is \( \boxed{6} \).

8. Verification:

   • Starting allowance: \( x = 6 \)
   • Money spent at the movies: \( \frac{1}{2} \times 6 = 3 \)
   • Amount left after movies: \( 6 - 3 = 3 \)
   • Amount after cleaning windows: \( 3 + 5 = 8 \)
   • End of the week amount: This matches the given ending amount of $8. Thus, our solution is correct.

Angela's weekly allowance is indeed \( \boxed{6} \).