Question

Three consecutive odd integers have a sum of 27. Find the integers.

Answer 1

`\sf \bf {\boxed {\mathbb {GIVEN:}}}`

Sum of three consecutive odd integers =
`27`

`\sf \bf {\boxed {\mathbb {TO\:FIND:}}}`

The values of the three integers.

`\sf \bf {\boxed {\mathbb {SOLUTION:}}}`

`\sf\purple{The\:three\:consecutive \:odd\:integers\:are\:7,\:9\:and\:11.}`

`\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}`

Let us assume the three consecutive odd integers to be
`x`,
`(x+2)` and
`(x+4)`.

As per the condition, we have

`Sum \: \: of \: \: the \: \: three \: \: consecutive \: \: odd \: \: integers = 27`

`➺ \: x + (x + 2) + (x + 4) = 27`

`➺ \: x + x + 2 + x + 4 = 27`

Now, collect the like terms.

`➺ \: (x + x + x) + (2 + 4) = 27`

`➺ \: 3x + 6 = 27`

`➺ \: 3x = 27 - 6`

`➺ \: 3x = 21`

`➺ \: x = (21)/(3) \\`

`➺ \: x = 7`

Therefore, the three consecutive odd integers whose sum is
`27` are
`\boxed{ 7 }`,
`\boxed{ 9 }` and
`\boxed{ 11 }` respectively.

`\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}`

`⇢ 7 + 9 + 11 = 27`

`⇢ 27 = 27`

⇢ L. H. S. = R. H. S.

`\sf\blue{Hence\:verified.}`

`\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}`