Question

1/3 of all the trick or treaters that came to your house were dressed as characters from Star Wars. 3/5 of those

dressed as characters from Star Wars were dressed as the character Darth Vader. What fraction of all trick or
treaters were dressed as Star Wars and were Darth Vader?

Answer 1

1/5

Explanation:

1/3 x 3/5 = 3/15

simplified to 1/5

Answer 2

1/5

Explanation:

Assuming the total number of all the trick or treaters that came to my house is N and the numbers of trick or treaters were dressed as characters from Star Wars is n.

Given that the portion of trick or treaters were dressed as characters from Star Wars, = 1/3 of all the trick or treaters.

`\Rightarrow n = \frac 1 3 N \cdots(i)`

Now, 3/5 of those dressed as characters from Star Wars were dressed as the character Darth Vader, so

The number of visitors that were dressed as the character Darth Vader

`= \frac 3 5 n \\\\`

`=\frac 3 5 * \frac 1 3 N` [ by using equation (i)]

`=\frac 1 5 N.`

Hence, the fraction of all trick or treaters were dressed as Star Wars and were Darth Vader is 1/5.