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3 years ago

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

Mathematics

1 answer:

jek_recluse [69]3 years ago

4 0

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

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.

$➺ \: (x + x + x) + (2 + 4) = 27$

$➺ \: 3x + 6 = 27$

$➺ \: 3x = 27 - 6$

$➺ \: 3x = 21$

$➺ \: x = \frac{21}{3} \\$

$➺ \: x = 7$

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.

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

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

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