The answer is $527 because 32% off is $248
<h3><u>Question:</u></h3>
Denzel earned money after school. He put 1/2 of this month's earnings into savings. He took the rest to spend at the amusement park. He spent 1/5 of this amount on popcorn and 3/4 of it on rides. What fraction of his earnings did he take to the park but not spend on rides or popcorn.
<h3><u>Answer:</u></h3>
fraction of money not spend in amusement park
<h3><u>Solution:</u></h3>
Let "x" be the total earnings
He put 1/2 of this month's earnings into savings
![\text{ savings} = \frac{1}{2} \text{ of } x](https://tex.z-dn.net/?f=%5Ctext%7B%20savings%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctext%7B%20of%20%7D%20x)
![\text{ savings} = \frac{1}{2}x = \frac{x}{2}](https://tex.z-dn.net/?f=%5Ctext%7B%20savings%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx%20%3D%20%5Cfrac%7Bx%7D%7B2%7D)
He took the rest to spend at the amusement park
![\text{ Remaining amount }= x - \frac{x}{2}\\\\\text{ Remaining amount } = \frac{2x - x}{2} = \frac{x}{2}](https://tex.z-dn.net/?f=%5Ctext%7B%20Remaining%20amount%20%7D%3D%20x%20-%20%5Cfrac%7Bx%7D%7B2%7D%5C%5C%5C%5C%5Ctext%7B%20Remaining%20amount%20%7D%20%3D%20%5Cfrac%7B2x%20-%20x%7D%7B2%7D%20%3D%20%5Cfrac%7Bx%7D%7B2%7D)
He spent 1/5 of this amount on popcorn and 3/4 of it on rides
![\text{ Amount spend on popcorn } = \frac{1}{5} \times \frac{x}{2} = \frac{x}{10}](https://tex.z-dn.net/?f=%5Ctext%7B%20Amount%20spend%20on%20popcorn%20%7D%20%3D%20%5Cfrac%7B1%7D%7B5%7D%20%5Ctimes%20%5Cfrac%7Bx%7D%7B2%7D%20%3D%20%5Cfrac%7Bx%7D%7B10%7D)
![\text{ amount spend on rides } = \frac{3}{4} \times \frac{x}{2} = \frac{3x}{8}](https://tex.z-dn.net/?f=%5Ctext%7B%20amount%20spend%20on%20rides%20%7D%20%3D%20%5Cfrac%7B3%7D%7B4%7D%20%5Ctimes%20%5Cfrac%7Bx%7D%7B2%7D%20%3D%20%5Cfrac%7B3x%7D%7B8%7D)
<em><u>So the fraction of money not spend in amusement park is:</u></em>
⇒ Remaining amount - (Amount spend on popcorn + amount spend on rides)
![\rightarrow \frac{x}{2} - (\frac{x}{10} + \frac{3x}{8})\\\\\rightarrow \frac{x}{2} - \frac{38x}{80}\\\\\rightarrow \frac{2x}{80} = \frac{x}{40}](https://tex.z-dn.net/?f=%5Crightarrow%20%5Cfrac%7Bx%7D%7B2%7D%20-%20%28%5Cfrac%7Bx%7D%7B10%7D%20%2B%20%5Cfrac%7B3x%7D%7B8%7D%29%5C%5C%5C%5C%5Crightarrow%20%5Cfrac%7Bx%7D%7B2%7D%20-%20%5Cfrac%7B38x%7D%7B80%7D%5C%5C%5C%5C%5Crightarrow%20%5Cfrac%7B2x%7D%7B80%7D%20%3D%20%5Cfrac%7Bx%7D%7B40%7D)
Thus
fraction of money not spend in amusement park
Answer:
x = 1/3 or x = 3/4
Step-by-step explanation:
Solve for x:
12 x^2 - 13 x + 3 = 0
The left hand side factors into a product with two terms:
(3 x - 1) (4 x - 3) = 0
Split into two equations:
3 x - 1 = 0 or 4 x - 3 = 0
Add 1 to both sides:
3 x = 1 or 4 x - 3 = 0
Divide both sides by 3:
x = 1/3 or 4 x - 3 = 0
Add 3 to both sides:
x = 1/3 or 4 x = 3
Divide both sides by 4:
Answer: x = 1/3 or x = 3/4
Answer:
x =68
Step-by-step explanation:
We know that x+22 = 90 because the sum of the two angles is a vertical angle to the right angle and vertical angles are equal.
x+22 =90
Subtract 22 from each side
x+22-22 = 90-22
x =68