Question

The sum of two consecutive even integr is 54. find the integers​

Answer 1

Answer:

26 and 28

Explanation:

1st integer = x

2nd integer = x + 2

 x + x + 2 = 54

2x + 2 = 54

2x = 52

 x = 26

 The 1st integer is 26.

The 2nd integer is 28.

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Answer 2

Correct Question-:

• 1 ) The sum of two consecutive even integers is 54. Find the integers.

AnswEr-:

• $\underline{\boxed{\star{\sf{\blue{ The \:two\:even\:consecutive \:integers\:are\:26\:and\:28 .}}}}}$

Explanation -:

• $\frak{Given \:-:}\begin{cases} & \sf{The \:sum \:of\: two \:consecutive\: even \:integers\: is\: 54 .} \end{cases}$

• $\frak{To\: Find \:-:}\begin{cases} & \sf{The \:\: two \: \:integers\: .} \end{cases}$

Now ,

• $\frak{Let's \:Assume \:-:}\begin{cases} \sf{Let\:the\:first\:integer\:be\:x .}&\\\\ \sf{Let\:the\:second\:integer\:be\:x+2.}\end{cases}$

• $\frak{According \:To\:The\:Question \:-:}\begin{cases} & \sf{ The \:sum \:of\: two \:consecutive\: even \:integers\: is\: 54 .} \end{cases}$

Then ,

• $\implies{\sf{\large {x + x + 2 = 54 }}}$

$\sf{\bf{\dag{Now\: Solving\: for\: X ,}}}$

• $\implies{\sf{\large {x + x + 2 = 54 }}}$
• $\implies{\sf{\large {2x + 2 = 54 }}}$
• $\implies{\sf{\large {2x= 54 - 2 }}}$
• $\implies{\sf{\large {2x = 52 }}}$
• $\implies{\sf{\large {x = \frac{52}{2} }}}$
• $\implies{\sf{\large {x = 26 }}}$

Then ,

• $\underline{\boxed{\star{\sf{\blue{ x = 26 }}}}}$

Now ,

• $\frak{Putting \:x=26\:-:}\begin{cases} \sf{\:The\:first\:integer\:is\:x= 26 .}&\\\\ \sf{\:The\:second\:integer\:is\:x+2 = 26 + 2 = 28.}\end{cases}$

Hence ,

• $\underline{\boxed{\star{\sf{\blue{ The \:two\:even\:consecutive \:integers\:are\:26\:and\:28 .}}}}}$

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♤ Verification ♤

• $\frak{Here \:-:}\begin{cases} \sf{\:The\:first\:integer\:is\:x .}&\\\\ \sf{\:The\:second\:integer\:is\:x+2.}\end{cases}$

• $\frak{According \:To\:The\:Question \:-:}\begin{cases} \sf{ The \:sum \:of\: two \:consecutive\: even \:integers\: is\: 54 .} \end{cases}$

Then ,

• $\implies{\sf{\large {x + x + 2 = 54 }}}$

Now ,

• $\underline{\boxed{\star{\sf{\blue{ x = 26 }}}}}$

$\sf{\bf{\dag{By \:Substituting\: the\: value -: ,}}}$

• $\implies{\sf{\large {26+ 26 + 2 = 54 }}}$
• $\implies{\sf{\large {26 + 28 = 54 }}}$
• $\implies{\sf{\large {54= 54 }}}$

Therefore,

• $\underline{\boxed{\star{\sf{\blue{ LHS = RHS }}}}}$
• $\underline{\boxed{\star{\sf{\blue{ Hence ,\: Verified }}}}}$

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