Question

The cost of 6/4 cups of coffee is 24/5 dollars. Find the cost of 1 cup of coffee.
16/5
13/5
24/5
12/5

Answer 1

To find the cost of 1 cup of coffee, we first need to determine the price per cup based on the given information.

We know that the cost of \( \frac{6}{4} \) cups of coffee is \( \frac{24}{5} \) dollars.

1. **Convert \( \frac{6}{4} \) to a simpler form**:

\[
\frac{6}{4} = \frac{3}{2}
\]

2. **Let \( x \) be the cost of 1 cup of coffee**. Then, the cost of \( \frac{3}{2} \) cups is given by:

\[
\frac{3}{2} \times x = \frac{24}{5}
\]

3. **To isolate \( x \)**, we can multiply both sides by \( \frac{2}{3} \) (the reciprocal of \( \frac{3}{2} \)):

\[
x = \frac{24}{5} \times \frac{2}{3}
\]

4. **Perform the multiplication**:

\[
x = \frac{24 \times 2}{5 \times 3} = \frac{48}{15}
\]

5. **Simplify \( \frac{48}{15} \)**:

\[
x = \frac{16}{5}
\]

Thus, the cost of 1 cup of coffee is \( \frac{16}{5} \) dollars.

The answer is:

\(\boxed{\frac{16}{5}}\)