Question

Denzel earned money after school delivering newspapers and doing yardwork. He put - of this month's earnings into his savings. He took the rest to spend at the amusement park. He spent of this amount on popcorn and of it on rides. What fraction of his amusement park money did he spend on rides and popcorn?

Answer 1

Question:

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.

Answer:

$\frac{1}{40}$ fraction of money not spend in amusement park

Solution:

Let "x" be the total earnings

He put 1/2 of this month's earnings into savings

$\text{ savings} = \frac{1}{2} \text{ of } x$

$\text{ savings} = \frac{1}{2}x = \frac{x}{2}$

He took the rest to spend at the amusement park

$\text{ Remaining amount }= x - \frac{x}{2}\\\\\text{ Remaining amount } = \frac{2x - x}{2} = \frac{x}{2}$

He spent 1/5 of this amount on popcorn and 3/4 of it on rides

$\text{ Amount spend on popcorn } = \frac{1}{5} \times \frac{x}{2} = \frac{x}{10}$

$\text{ amount spend on rides } = \frac{3}{4} \times \frac{x}{2} = \frac{3x}{8}$

So the fraction of money not spend in amusement park is:

⇒ Remaining amount - (Amount spend on popcorn + amount spend on rides)

$\rightarrow \frac{x}{2} - (\frac{x}{10} + \frac{3x}{8})\\\\\rightarrow \frac{x}{2} - \frac{38x}{80}\\\\\rightarrow \frac{2x}{80} = \frac{x}{40}$

Thus $\frac{1}{40}$ fraction of money not spend in amusement park