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 \( x \) be the amount of Angela's weekly allowance.

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

2. Spending at the Movies: She spends half of her weekly allowance at the movies. Therefore, the amount spent is \( \frac{1}{2}x \), and the amount she has left after this spending is: \[ x - \frac{1}{2}x = \frac{1}{2}x \]

3. Earning Money: Angela earns an additional $5 by cleaning windows. So now, her total amount after earning that money is: \[ \frac{1}{2}x + 5 \]

4. Ending Amount: We know that at the end of the week, Angela has $8. Thus, we can set up the equation: \[ \frac{1}{2}x + 5 = 8 \]

5. Solving the Equation:

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

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

Verification:

• Starting amount: \( 6 \) dollars.
• Spent at the movies: \( \frac{1}{2} \times 6 = 3 \) dollars, leaving her with \( 6 - 3 = 3 \) dollars.
• Earned from cleaning: \( 3 + 5 = 8 \) dollars.
• Ends the week with \( 8 \) dollars, which checks out.

Thus, the calculation confirms that her weekly allowance is indeed \( \boxed{6} \) dollars.