Question

William and Daphne both have crackers for snacks. The ratio of Williams crackers to Daphne’s is 3 to 5 if there are 48 crackers total how many crackers does Daphne have use the tape diagram to organize your thinking?

Answer 1

To solve the problem using a ratio and total amount, we can follow these steps:

1. **Understanding the Ratio**: The ratio of William's crackers to Daphne’s crackers is given as 3 to 5. This means that for every 3 parts of crackers that William has, Daphne has 5 parts.

2. **Total Parts in the Ratio**: To find the total number of parts in the ratio, we add the parts:
\[
3 + 5 = 8 \text{ parts}
\]

3. **Finding the Value of One Part**: Given that the total number of crackers is 48, we find the value of one part by dividing the total number of crackers by the total number of parts:
\[
\text{Value of one part} = \frac{48}{8} = 6
\]

4. **Calculating the Number of Crackers for Each Person**: Now that we have the value of one part, we can find how many crackers each person has:
- **William's Crackers**:
\[
\text{William's crackers} = 3 \text{ parts} \times 6 = 18
\]
- **Daphne's Crackers**:
\[
\text{Daphne's crackers} = 5 \text{ parts} \times 6 = 30
\]

5. **Summary**:
- William has 18 crackers.
- Daphne has 30 crackers.

Thus, Daphne has **30 crackers**.

You can visualize this with a tape diagram by drawing 3 segments representing William's parts (each segment being 6 crackers long) and 5 segments representing Daphne's parts. This reinforces the ratio visually.