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Algebra Difficulty 2.2 Junior Find the answer

In a cafeteria line, the number of people ahead of Kaukab is equal to two times the number of people behind her. There are nn people in the line. What is a possible value of nn?

A number or a short expression. Spacing and $ signs are ignored.

Solution

Suppose that there are pp people behind Kaukab. This means that there are 2p2p people ahead of her. Including Kaukab, the total number of people in line is n=p+2p+1=3p+1n = p + 2p + 1 = 3p + 1, which is one more than a multiple of 3. Of the given choices (23,20,24,21,25)(23, 20, 24, 21, 25), the only one that is one more than a multiple of 3 is 25, which equals 3×8+13 \times 8 + 1. Therefore, a possible value for nn is 25.

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