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CEMC Cayley, 2024

Algebra Difficulty 1.3 Junior Find the answer Canada

The sum of five consecutive odd integers is $125$ . The smallest of these integers
is

Pick one

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 $21$ . (This means that the five odd
integers are $21$ , $23$ , $25$ , $27$ , $29$ .)

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