Question

The sum of three consecutive odd integers is at most 123. Find the pair with the greatest sum

Answer 1

Answer:

a1 = 39, a2 = 41, a3 = 43

The pair with the greatest sum is a2 + a3 = 41 + 43 = 84

Step-by-step explanation:

Let the first integer be a1 = a.

Let the second odd integer be a2 = a + 2

Let the third odd integer be a3 = (a + 2) + 2 = a + 4

The sum of three consecutive odd integers is 123.

123 = a1 + a2 + a3

123 = a + (a + 2) + (a + 4)

123 = 3a + 6

117 = 3a

a = 39

a1 = a = 39

a2 = a + 2 = 39 + 2 = 41

a3 = a + 4 = 39 + 4 = 43

The pair with the greatest sum is a2 + a3 = 41 + 43 = 84