Question

At the donut shop 1/2 of their donuts have frosting. Of the donuts with frosting, 3/4 of them have sprinkles. How many donuts have both frosting and sprinkles?

Answer 1

To find out how many donuts have both frosting and sprinkles, we can work through the information step by step. However, we need to know the total number of donuts in the shop to provide a numerical answer.

Let's denote the total number of donuts as \( N \).

1. **Donuts with Frosting:**
Since half of the donuts have frosting, the number of donuts with frosting is:
\[
\text{Donuts with frosting} = \frac{1}{2} N
\]

2. **Donuts with Sprinkles (and Frosting):**
Of the donuts with frosting, 3/4 have sprinkles. Therefore, the number of donuts that have both frosting and sprinkles is:
\[
\text{Donuts with frosting and sprinkles} = \frac{3}{4} \times \text{(Donuts with frosting)} = \frac{3}{4} \times \frac{1}{2} N
\]

This simplifies to:
\[
\text{Donuts with frosting and sprinkles} = \frac{3}{8} N
\]

So, the number of donuts that have both frosting and sprinkles is \(\frac{3}{8}N\).

To get an actual number, you would need to know the total number of donuts \( N \). For example, if there are 32 donuts in total, then:
\[
\frac{3}{8} \times 32 = 12
\]
Thus, there would be 12 donuts with both frosting and sprinkles.