Question

Zachary and Grayson are collecting clothes for a clothing drive. Grayson collected 3/4 as many clothes as Zachary did. If Zachary collected 2/5 of a bag of clothes, how many bags of clothes did Grayson 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 Grayson collected, we start by determining how many clothes Zachary collected.

Zachary collected \( \frac{2}{5} \) of a bag of clothes.

Grayson collected \( \frac{3}{4} \) as many clothes as Zachary did. To find the amount Grayson collected, we multiply Zachary's collection by \( \frac{3}{4} \):

\[
\text{Grayson's collection} = \frac{3}{4} \times \frac{2}{5}
\]

Now, we perform the multiplication of the two fractions:

\[
\frac{3}{4} \times \frac{2}{5} = \frac{3 \times 2}{4 \times 5} = \frac{6}{20}
\]

Next, we simplify \( \frac{6}{20} \):

Both 6 and 20 can be divided by their greatest common divisor, which is 2:

\[
\frac{6 \div 2}{20 \div 2} = \frac{3}{10}
\]

Therefore, Grayson collected \( \frac{3}{10} \) of a bag of clothes.

Thus, the answer is:

\[
\frac{3}{10} \text{ bags}
\]