Question

The sum of two consecutive even integers is 54. Find the integers.
The sum of an integer and twice the
Find the two integers.​

Answer 1

Question:-

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

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Given:-

• Sum of two consecutive even integers is 54.

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To find:-

• Find the integers.

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Solution:-

• Let the first integer be x.
• Let the second integer be x + 2.

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$\large{\tt{\longmapsto{x + x + 2 = 54}}}$

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$\large{\tt{\longmapsto{2x + 2 = 54}}}$

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$\large{\tt{\longmapsto{2x = 54 - 2}}}$

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$\large{\tt{\longmapsto{2x = 52}}}$

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$\large{\tt{\longmapsto{x = \dfrac{52}{2}}}}$

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$\large{\tt{\longmapsto{\boxed{\red{x = 26}}}}}$

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Hence,

• First integer = 26
• Second integer = x + 2 = 28

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Verification:-

$\large{\tt{\longmapsto{x + x + 2 = 54}}}$

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$\large{\tt{\longmapsto{26 + 28 = 54}}}$

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$\large{\tt{\longmapsto{\boxed{\orange{54 = 54}}}}}$

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Hence Verified

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⠀⠀

Correct Question:-

• The sum of an integer and twice the next integer is 41. Find the two integers.

⠀

Given:-

Sum of an integer and twice the next integer is 41.

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To find:-

The two integers.

⠀

Solution:-

• Let the first integer be x.
• Let the second integer be x + 1.

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$\large{\tt{\longmapsto{x + 2(x + 1) = 41}}}$

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$\large{\tt{\longmapsto{3x + 2 = 41}}}$

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$\large{\tt{\longmapsto{3x = 41 - 2}}}$

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$\large{\tt{\longmapsto{3x = 39}}}$

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$\large{\tt{\longmapsto{x = \dfrac{39}{3}}}}$

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$\large{\tt{\longmapsto{\boxed{\red{x = 13}}}}}$

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Hence,

• First integer = 13
• Second integer = x + 1 = 14

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Verification:-

$\large{\tt{\longmapsto{x + x + 1 = 41}}}$

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$\large{\tt{\longmapsto{13 + 14 = 41}}}$

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$\large{\tt{\longmapsto{\boxed{\orange{41 = 41}}}}}$

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Hence Verified

Answer 2

AnswEr-:

• 1 ) $\underline{\boxed{\star{\sf{\blue{ The \:two\:even\:consecutive \:integers\:are\:26\:and\:28 .}}}}}$
• 2 ) $\underline{\boxed{\star{\sf{\blue{ The \:two\:even\:\:integers\:are\:13\:and\:14 .}}}}}$

Correct Question-:

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

AnswEr-:

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 ,

• Let the First integer be x .
• Let the second integer be x +2

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

Then ,

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

Now 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 ,

• First Integer = x = 26
• Second integer = x + 2 = 26 + 2 = 28

Hence ,

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

________________________________________

♤ Verification ♤

• The First integer is x .
• The second integer is x +2

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

Then ,

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

Now ,

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

By Substituting the value -:

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

Therefore,

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

__________________________

Correct question -:

• 2 ) The sum of an integer and twice the next integer is 41 . Find the two integers ?

AnswEr-:

Explanation-:

$\frak{Given \:-:}\begin{cases} & \sf{ The \:sum\: of \:an\: integer \:and \:twice\: the\: next\: integer\: is\: 41 .} \end{cases}$

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

Now ,

• Let the first integer be x .
• The second integer is X + 1

According to the question-:

• $\implies{\sf{\large {x + 2 (x +1) = 41 }}}$
• $\implies{\sf{\large { 3x +2 = 41 }}}$
• $\implies{\sf{\large {3x= 41-2 }}}$
• $\implies{\sf{\large {3x = 39 }}}$
• $\implies{\sf{\large {x= \frac{39}{3} }}}$
• $\implies{\sf{\large {x = 13 }}}$

Therefore,

• $\underline{\boxed{\star{\sf{\blue{ x = 13}}}}}$

Now ,

• First Integer = x = 13 .
• Second Integer = x + 1 = 13 + 1 = 14

Hence ,

• $\underline{\boxed{\star{\sf{\blue{ The \:two\:even\:\:integers\:are\:13\:and\:14 .}}}}}$

___________________________________

♤ Verification ♤

• The First integer is x .
• The second integer be x + 1.

$\frak{According \:To\:The\:Question \:-:}\begin{cases} & \sf{The \:sum\: of \:an\: integer \:and \:twice\: the\: next\: integer\: is\: 41 .} \end{cases}$

Now ,

• $\implies{\sf{\large {x + 2 (x +1) = 41 }}}$

Here ,

• $\underline{\boxed{\star{\sf{\blue{ x = 13}}}}}$

Now,

• $\implies{\sf{\large {13 + 2 (13 +1) = 41 }}}$
• $\implies{\sf{\large {13 + 26 + 2 = 41 }}}$
• $\implies{\sf{\large {13 + 28 = 41 }}}$
• $\implies{\sf{\large {41 = 41 }}}$

Therefore ,

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

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