Question

Every day, the Oliver Family Restaurant serves 1 3/4 bottles of soda to their customers. How many days will 3 1/2 bottles of soda last?

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

Answer 1

To find out how many days 3 1/2 bottles of soda will last when the Oliver Family Restaurant serves 1 3/4 bottles of soda each day, we need to perform the division of the total bottles by the daily usage.

First, let's convert the mixed numbers into improper fractions:

1. Convert \(3 \frac{1}{2}\) into an improper fraction:
\[
3 \frac{1}{2} = 3 \times 2 + 1 = 6 + 1 = 7 \quad \text{so} \quad 3 \frac{1}{2} = \frac{7}{2}
\]

2. Convert \(1 \frac{3}{4}\) into an improper fraction:
\[
1 \frac{3}{4} = 1 \times 4 + 3 = 4 + 3 = 7 \quad \text{so} \quad 1 \frac{3}{4} = \frac{7}{4}
\]

Next, we'll divide \( \frac{7}{2} \) by \( \frac{7}{4} \):
\[
\frac{7}{2} \div \frac{7}{4} = \frac{7}{2} \times \frac{4}{7}
\]

Notice that \(7\) in the numerator and denominator cancels out:
\[
= \frac{4}{2} = 2
\]

Therefore, \(3 \frac{1}{2}\) bottles of soda will last for \(2\) days when \(1 \frac{3}{4}\) bottles are served each day.

So, the final answer is:

\[
\boxed{2}
\]