CEMC Cayley

Algebra Difficulty 2.0 Junior Find the answer

The sum of five consecutive odd integers is 125. What is the smallest of these integers?

Your answer

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

Solution

Suppose that the smallest of the five odd integers is $x$ . Since consecutive odd integers differ by 2, the other four odd integers are $x+2, x+4, x+6$ , and $x+8$ . Therefore, $x + (x+2) + (x+4) + (x+6) + (x+8) = 125$ . From this, we obtain $5x + 20 = 125$ and so $5x = 105$ , which gives $x = 21$ . Thus, the smallest of the five integers is 21.

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