Question

Matt and John are collecting clothes for a clothing drive. John collected 1/6 as many clothes as Matt did. If Matt collected 7 1/5 bags of clothes, how many bags of clothes did John collect?

Write your answer as a fraction or as a whole or mixed number.

bags

Answer 1

To find out how many bags of clothes John collected, we start by determining how many bags Matt collected.

Matt collected \( 7 \frac{1}{5} \) bags. We can convert this mixed number to an improper fraction:

\[
7 \frac{1}{5} = 7 + \frac{1}{5} = \frac{35}{5} + \frac{1}{5} = \frac{36}{5}
\]

Now that we know Matt collected \( \frac{36}{5} \) bags, we can find how many bags John collected. According to the problem, John collected \( \frac{1}{6} \) as many bags as Matt did. Therefore, we calculate:

\[
\text{John's bags} = \frac{1}{6} \times \frac{36}{5} = \frac{36}{30}
\]

Now we can simplify \( \frac{36}{30} \):

\[
\frac{36}{30} = \frac{6}{5}
\]

Next, we can convert \( \frac{6}{5} \) to a mixed number:

\[
\frac{6}{5} = 1 \frac{1}{5}
\]

Thus, the number of bags of clothes that John collected is:

\[
\boxed{1 \frac{1}{5}} \text{ bags}
\]