[tex]\sf \bf {\boxed {\mathbb {GIVEN:}}}[/tex]
Sum of three consecutive odd integers = [tex]27[/tex]
[tex]\sf \bf {\boxed {\mathbb {TO\:FIND:}}}[/tex]
The values of the three integers.
[tex]\sf \bf {\boxed {\mathbb {SOLUTION:}}}[/tex]
[tex]\sf\purple{The\:three\:consecutive \:odd\:integers\:are\:7,\:9\:and\:11.}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]
Let us assume the three consecutive odd integers to be [tex]x[/tex], [tex](x+2)[/tex] and [tex](x+4)[/tex].
As per the condition, we have
[tex]Sum \: \: of \: \: the \: \: three \: \: consecutive \: \: odd \: \: integers = 27[/tex]
[tex]➺ \: x + (x + 2) + (x + 4) = 27[/tex]
[tex]➺ \: x + x + 2 + x + 4 = 27[/tex]
Now, collect the like terms.
[tex]➺ \: (x + x + x) + (2 + 4) = 27[/tex]
[tex]➺ \: 3x + 6 = 27[/tex]
[tex]➺ \: 3x = 27 - 6[/tex]
[tex]➺ \: 3x = 21[/tex]
[tex]➺ \: x = \frac{21}{3} \\[/tex]
[tex]➺ \: x = 7[/tex]
Therefore, the three consecutive odd integers whose sum is [tex]27[/tex] are [tex]\boxed{ 7 }[/tex], [tex]\boxed{ 9 }[/tex] and [tex]\boxed{ 11 }[/tex] respectively.
[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}[/tex]
[tex]⇢ 7 + 9 + 11 = 27[/tex]
[tex]⇢ 27 = 27[/tex]
⇢ L. H. S. = R. H. S.
[tex]\sf\blue{Hence\:verified.}[/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}[/tex]
