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Find three consecutive even integers whose sum is 84.
A26, 28, and 30
B24, 26, and 28
C28, 30, and 32
D26, 30, and 34
Answer & Solution
Correct answer: A. 26, 28, and 30
1. Consecutive even integers increase by two each time, so if the first is n, the next two are n plus 2 and n plus 4.
2. The sum translates to n plus (n plus 2) plus (n plus 4) equals 84.
3. Combine like terms: 3n plus 6 equals 84.
4. Subtract 6 and divide by 3 to get n equals 26, so the integers are 26, 28, and 30.
5. Check: 26 plus 28 plus 30 equals 84.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 3 "Math Models", section 3.1 Use a Problem-Solving Strategy_
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