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 five dollars. what is her weekly allowance if she ended the week with eight dollars solve using arithmetic or algebra and explain your steps
Let's assume Angela's weekly allowance is $x.
According to the problem, she spent half of her weekly allowance at the movies. Therefore, she spent (1/2)x dollars at the movies.
After going to the movies, Angela earned $5 by cleaning the windows. So, she has [(1/2)x + $5] left.
We are given that Angela ended the week with $8. So, we can write the equation:
[(1/2)x + $5] = $8
To solve for x, we can start by subtracting $5 from both sides of the equation:
(1/2)x = $8 - $5
(1/2)x = $3
Now, to isolate x, we multiply both sides of the equation by 2:
x = 2 * $3
x = $6
Therefore, Angela's weekly allowance is $6.
Let's assume Angela's weekly allowance is represented by the variable "x." According to the given information, she spent half of her weekly allowance at the movies. Therefore, she spent (1/2)x dollars at the movies.
After spending this amount, her remaining allowance is (1/2)x. Angela's parents let her clean the windows in the house for $5, so her remaining allowance would increase by $5.
So, her remaining allowance after cleaning the windows is (1/2)x + $5. We are given that she ended the week with $8, so we can set up the equation:
(1/2)x + $5 = $8
To solve this equation, we'll isolate the variable x.
Subtracting $5 from both sides of the equation, we have:
(1/2)x = $8 - $5
(1/2)x = $3
To eliminate the fraction, we can multiply both sides of the equation by 2:
2 * (1/2)x = 2 * $3
x = $6
Therefore, Angela's weekly allowance is $6.
To solve this problem using arithmetic, let's follow the steps and track Angela's earnings and expenses.
1. Let's represent Angela's weekly allowance as "x" (unknown value).
2. Angela spends half of her weekly allowance at the movies. This means she spent (1/2)x dollars.
3. After going to the movies, Angela earns 5 dollars by cleaning the windows in her house.
4. Therefore, Angela's total earnings for the week are: (x - (1/2)x + 5) dollars.
5. The problem states that Angela ended the week with 8 dollars. Hence, we can set up the following equation based on her earnings:
(x - (1/2)x + 5) = 8.
6. Let's solve the equation:
Simplifying the left side: x - (1/2)x + 5 = 8,
Combining like terms: (1 - 1/2)x + 5 = 8,
Simplifying fractional coefficient: (1/2)x + 5 = 8,
Moving 5 to the other side: (1/2)x = 8 - 5 = 3,
Simplifying further: (1/2)x = 3,
Multiply both sides by 2 to isolate x: x = 3 * 2 = 6.
Therefore, Angela's weekly allowance is 6 dollars.
To solve this problem using algebra, we followed the steps of gathering the given information, defined the unknown variable, and formed an equation based on the given information. We then simplified the equation by combining like terms and isolating the variable to find the solution.