CEMC Cayley

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 $n$ people in the line. What is a possible value of $n$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

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

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