To solve the problem using a ratio and total amount, we can follow these steps:
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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.
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Total Parts in the Ratio: To find the total number of parts in the ratio, we add the parts: \[ 3 + 5 = 8 \text{ parts} \]
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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: \[ \text{Value of one part} = \frac{48}{8} = 6 \]
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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: \[ \text{Daphne's crackers} = 5 \text{ parts} \times 6 = 30 \]
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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.
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