Question

Yesterday, Paula's Doughnut Shop sold 1/5 as many chocolate doughnuts as cinnamon doughnuts. If they sold 1/4 of a tray of cinnamon doughnuts, how many trays of chocolate doughnuts did they sell?

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

trays

Answer 1

Let the number of trays of cinnamon doughnuts sold be \( x \). According to the problem, they sold \( \frac{1}{4} \) of a tray of cinnamon doughnuts. Therefore, we have:

\[
x = \frac{1}{4}
\]

Now, according to the information given, Paula's Doughnut Shop sold \( \frac{1}{5} \) as many chocolate doughnuts as they sold cinnamon doughnuts.

To find the number of trays of chocolate doughnuts sold, we compute:

\[
\text{Trays of chocolate doughnuts} = \frac{1}{5} \times x
\]

Substituting \( x = \frac{1}{4} \) into this equation gives:

\[
\text{Trays of chocolate doughnuts} = \frac{1}{5} \times \frac{1}{4}
\]

To multiply the fractions, we multiply the numerators and the denominators:

\[
= \frac{1 \times 1}{5 \times 4} = \frac{1}{20}
\]

Thus, the number of trays of chocolate doughnuts sold is:

\[
\boxed{\frac{1}{20}}
\]