16. 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.(3 points)
Let's say Angela's weekly allowance is x.
She spent half of her weekly allowance at the movies, which is 0.5x.
After the movie, she has 0.5x left.
Her parents let her clean the windows and earn $5, so her total money at the end of the week is 0.5x + 5.
According to the given information, she ended the week with $8, so we have the equation:
0.5x + 5 = 8
Subtracting 5 from both sides of the equation, we get:
0.5x = 3
Dividing both sides of the equation by 0.5, we get:
x = 6
Therefore, Angela's weekly allowance is $6.
Let's solve this using algebra.
Let's assume Angela's weekly allowance is the variable "x."
According to the information given, Angela spent half of her weekly allowance at the movies, so she spent (1/2)x dollars.
Then, Angela earned $5 by cleaning the windows.
If we add the money Angela earned and subtract the money she spent from her original weekly allowance, we should get the amount she ended the week with, which is $8.
So, we can create the following equation:
Original weekly allowance - money spent + money earned = money left at the end of the week
x - (1/2)x + $5 = $8
To solve for x, we simplify the equation:
(1/2)x + $5 = $8
(1/2)x = $8 - $5
(1/2)x = $3
To solve for x, we multiply both sides of the equation by 2:
2 * [(1/2)x] = 2 * $3
x = $6
Therefore, Angela's weekly allowance is $6.
To find Angela's weekly allowance, let's represent it by the variable 'x'.
According to the given information:
- Angela started the week with her weekly allowance, which is 'x'.
- She spent half of her weekly allowance at the movies, which would be 'x/2'.
- She earned an additional $5 by cleaning the windows.
We can create an equation based on the information given:
x - (x/2) + 5 = 8
Now, let's solve the equation step by step:
1. Distribute the negative sign to the terms inside the parentheses:
x - x/2 + 5 = 8
2. To simplify, we need to find a common denominator for the fraction:
The common denominator is 2, so we multiply 5 by 2 to get 10:
x - (x/2) + 10/2 = 8
3. Combine like terms on the left side of the equation:
To add x and x/2, we need to find a common denominator, which is 2:
(2x/2) - (x/2) + 10/2 = 8
(2x - x)/2 + 10/2 = 8
4. Simplify further:
(x/2) + 10/2 = 8
(x + 10)/2 = 8
5. Multiply both sides of the equation by 2 to eliminate the fraction:
2(x + 10)/2 = 8 * 2
x + 10 = 16
6. Subtract 10 from both sides of the equation to solve for x:
x + 10 - 10 = 16 - 10
x = 6
The solution to the equation is x = 6. Therefore, Angela's weekly allowance is $6.