Angelica earns a weekly allowance at the start of each week she started the week with just her weekly allowance then she spent half a 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 $8 solve using arithmetic or algebra and explain your steps
Let's assume the weekly allowance as 'x'.
According to the given information, Angelica spent half of one weekly allowance at the movies. So, she spent (1/2)*x = x/2 at the movies.
Then, Angelica earned $5 for cleaning the windows in the house.
Therefore, her total earnings for the week would be her allowance plus the money earned from cleaning the windows: x + $5.
Since she ended the week with $8, we can set up the equation:
x + $5 = $8
Subtracting $5 from both sides of the equation:
x = $8 - $5
x = $3
Thus, Angelica's weekly allowance is $3.
Let's solve this problem step-by-step.
Step 1: Let x be Angelica's weekly allowance.
Step 2: Angelica spent half of her weekly allowance at the movies, which is (1/2) * x.
Step 3: After spending (1/2) * x at the movies, she earned $5 by cleaning the windows.
Step 4: Therefore, her total amount at the end of the week is (x - (1/2) * x) + $5 = (1/2) * x + $5.
Step 5: According to the problem, her total amount at the end of the week is $8.
Step 6: So, we can set up the equation (1/2) * x + $5 = $8.
Step 7: Simplifying the equation, (1/2) * x = $8 - $5.
Step 8: (1/2) * x = $3.
Step 9: To solve for x, we multiply both sides of the equation by 2: x = $6.
Therefore, Angelica's weekly allowance is $6.
To find out Angelica's weekly allowance, we can use algebraic equations. Let's assume her weekly allowance as 'x'.
According to the problem, Angelica spends half of her weekly allowance at the movies, which means she spent (1/2)x dollars. Then, she earns an additional 5 dollars by cleaning windows.
Now, we can set up an equation to represent her total earnings for the week:
Total earnings = Starting allowance - Amount spent + Amount earned
8 = x - (1/2)x + 5
To simplify the equation further, we can combine like terms:
8 = (1/2)x + 5
Next, we can isolate the variable 'x' by subtracting 5 from both sides of the equation:
8 - 5 = (1/2)x
3 = (1/2)x
Finally, we can solve for 'x' by multiplying both sides of the equation by 2:
2 * 3 = 2 * (1/2)x
6 = x
Therefore, Angelica's weekly allowance is $6.