To determine the greatest number of plates Lexi can prepare without having any food left over, we need to find the greatest common divisor (GCD) of the number of crackers and the number of cheese slices.
Lexi has:
- 48 crackers
- 24 slices of cheese
We will calculate the GCD of 48 and 24.
Here are the steps to find the GCD:
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List the factors of 48:
- The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
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List the factors of 24:
- The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24.
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Identify the common factors:
- The common factors of 48 and 24 are: 1, 2, 3, 4, 6, 8, 12, 24.
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Determine the greatest common factor:
- The greatest common factor from those common factors is 24.
Thus, the greatest number of plates Lexi can prepare, with each plate having the same number of crackers and cheese slices and without having any food left over, is 24.
Verification:
- If Lexi makes 24 plates:
- Each plate will have \( \frac{48 \text{ crackers}}{24 \text{ plates}} = 2 \text{ crackers per plate} \).
- Each plate will have \( \frac{24 \text{ slices of cheese}}{24 \text{ plates}} = 1 \text{ slice of cheese per plate} \).
Since each plate has 2 crackers and 1 slice of cheese, and there are no leftovers, the calculation is correct.
Therefore, the greatest number of plates Lexi can prepare is 24.