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At a party, the cheese pizza is cut into 10 slices and the veggie pizza is cut into 20 slices. If the host wants to serve identical platters that contain the same combination of cheese and veggie slices, with no slices left over, what is the greatest number of platters the host can prepare?

Question

At a party, the cheese pizza is cut into 10 slices and the veggie pizza is cut into 20 slices. If the host wants to serve identical platters that contain the same combination of cheese and veggie slices, with no slices left over, what is the greatest number of platters the host can prepare?

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Solution

To solve this problem, we need to find the greatest common divisor (GCD) of the number of cheese pizza slices (10) and veggie pizza slices (20). The GCD is the largest number that can divide both numbers without leaving a remainder.

Step 1: List the divisors of each number. The divisors of 10 are: 1, 2, 5, 10. The divisors of 20 are: 1, 2, 4, 5, 10, 20.

Step 2: Identify the common divisors. The common divisors are: 1, 2, 5, 10.

Step 3: The greatest common divisor is the largest of these, which is 10.

So, the host can prepare 10 platters, each with 1 slice of cheese pizza and 2 slices of veggie pizza.

This problem has been solved

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