# The sum of 3 consecutive odd integers is 87. What are the consecutive integers?

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We are asked to find 3 consecutive odd integers that have a sum of 87.

=>  let x = the first odd integer

=>  let x + 2 = the second odd integer

=>  let x + 4 = the third odd integer

Write the equation to solve.

=> x + x + 2 + x + 4 = 87

=> 3x + 6 = 87

=> 3x = 81

=> x = 27  (first odd integer)

=> x + 2 = 29  (second odd integer)

=> x + 4 = 31 (third odd integer)

The consecutive odd integers with a sum of 87 are the following:  27, 29, 31.

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Let the consecutive odd integers be: 2k+1 , 2k+3 , 2k+5

The sum of these consecutive integers is 87:

2k + 1 + 2k + 3 + 2k + 5 = 87

We'll combine like terms:

6k + 9 = 87

We'll divide by 3:

2k + 3 = 29

We'll isolate 2k to the left side:

2k = 29 - 3

2k = 26 => k = 13

The consecutive odd integers are:

2k + 1 = 26 + 1 = 27

2k + 3 = 26 + 3 = 29

2k + 5 = 26+5 = 31

The requested consecutive odd integers whose sum is 87, are: 27 , 29 , 31.

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