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.
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.
Let's assume Angela's weekly allowance as "x" dollars.
According to the problem, she spent half of her weekly allowance at the movies. Therefore, she spent (1/2)x dollars.
She then earned $5 by cleaning the windows in the house. So, her earnings would be (1/2)x + 5 dollars.
The problem states that she ended the week with $8. So, her remaining money would be x - ((1/2)x + 5) = 8.
Let's solve this equation step-by-step:
x - (1/2)x - 5 = 8
Multiplying both sides by 2 to eliminate the fraction:
2x - x - 10 = 16
Simplifying:
x - 10 = 16
Adding 10 to both sides:
x = 26
Therefore, Angela's weekly allowance is $26.
To solve this problem, we can use algebra. Let's assume Angela's weekly allowance is represented by the variable "x".
According to the problem, Angela starts the week with her weekly allowance, spends half of it at the movies, and earns $5 by cleaning the windows. After all this, she ends the week with $8.
We can express this situation in an equation:
x - (1/2)x + 5 = 8
Let's simplify the equation:
x/2 + 5 = 8 (by subtracting (1/2)x from x)
Now, we'll isolate the variable x by moving the constant term (5) to the other side of the equation:
x/2 = 8 - 5 (by subtracting 5 from both sides)
x/2 = 3
To solve for x, we can multiply both sides of the equation by 2 to eliminate the fraction:
2 * (x/2) = 2 * 3
x = 6
Therefore, Angela's weekly allowance is $6.