Question

Every day, the Bryant Family Restaurant serves 5/6 of a bottle of soda to their customers. How many days will 2 1/2 bottles of soda last?

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

Answer 1

To determine how many days 2 1/2 bottles of soda will last when the Bryant Family Restaurant serves 5/6 of a bottle per day, we first need to convert 2 1/2 bottles into an improper fraction.

2 1/2 can be converted as follows:

\[
2 \times 2 + 1 = 4 + 1 = 5 \quad \text{(so, } 2 \frac{1}{2} = \frac{5}{2} \text{)}
\]

Now, we have \(\frac{5}{2}\) bottles of soda.

Next, we want to find out how many days this amount of soda will last given the daily consumption rate of \(\frac{5}{6}\) of a bottle:

To find the number of days, we can set up the following division:

\[
\text{Number of days} = \frac{\text{Total soda}}{\text{Daily soda}} = \frac{\frac{5}{2}}{\frac{5}{6}}
\]

Dividing by a fraction is the same as multiplying by its reciprocal:

\[
\frac{5}{2} \div \frac{5}{6} = \frac{5}{2} \times \frac{6}{5}
\]

Now, we can simplify:

\[
= \frac{5 \times 6}{2 \times 5} = \frac{30}{10} = 3
\]

Thus, 2 1/2 bottles of soda will last for \( \boxed{3} \) days.