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Two consecutive integers have a sum of 195. Find the integeres

Answer :

THEAMETHYSTGO

Hey ! there

Answer:

  • First Integer is 97

  • Second Integer is 98

Step-by-step explanation:

The question says that two consecutive Integer have a sum of 195 . And we are asked to find the integers.

For finding integers we are assuming them . So ,

  • Let the first integer be x .

  • Let the second integer be x + 1 ( This is because in question it's given that they are consecutive integers )

Solution : -

According to question ,

  • First Integer + Second Integer = 195

So ,

[tex] \dashrightarrow \qquad \: x + x + 1 = 195[/tex]

Step 1 : Adding like terms ( x and x ) on left side :

[tex] \dashrightarrow \qquad \: 2x + 1 = 195[/tex]

Step 2 : Subtracting 1 on both sides :

[tex] \dashrightarrow \qquad \: 2x + \cancel{1} - \cancel{1} = 195 - 1[/tex]

Simplifying it ,

[tex] \dashrightarrow \qquad \: 2x = 194[/tex]

Step 3 : Dividing with 2 on both sides :

[tex] \dashrightarrow \qquad \: \dfrac{ \cancel{2}x}{ \cancel{ 2}} = \cancel{\dfrac{194}{2} }[/tex]

On further calculations , We get :

[tex] \dashrightarrow \qquad \: \purple{\underline{\boxed{\frak{ x = 97}}}} \quad \: \bigstar[/tex]

We know that ,

  • x = first number

✰ Therefore , first number is 97 .

  • x + 1 = second number
  • 97 + 1
  • 98

✰ Therefore , second number is 98.

Verifying : -

Now , we are verifying our answer by substituting value of first and second number and equating it with 195 . So ,

  • 97 + 98 = 195

  • 195 = 195

  • L.H.S = R.H.S

  • Hence , Verified .

Therefore , our solution is correct .

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[tex]\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]

                Two consecutive integers have a sum of 195. Find the integers

[tex]\blue{\textsf{\textbf{\underline{\underline{Answer:-}}}}[/tex]

The integers are 97 and 98.

[tex]\blue{\textsf{\textbf{\underline{\underline{How to Solve:-}}}}[/tex]

                 If integers are [tex]\textbf{consecutive,}[/tex] they stand right next to each other.

Example:- 7 and 8. 7 and 8 are consecutive integers because they stand right next to each other.

Now, let the integer be n.

The integer next to n is 1 greater than n, or n+1.

So we set up the following equation:-

[tex]\bigstar{\fbox{n+n+1=195}[/tex]

[tex]\textsf{\underline}}[/tex]Add the n's:-

[tex]\Longrightarrow[/tex] [tex]\sf{2n+1=195}[/tex]

Subtract 1 on both sides:

[tex]\sf{2n=195-1}[/tex]

[tex]\sf{2n=194}[/tex]

Divide by 2 on both sides:-

[tex]\bigstar{\fbox{n=97}[/tex]

Now that we've found the first integer, finding the second integer is easy, because we can subtract the first integer from the sum of both integers:-

195-97=98

So the second integer is 98.

Quick Check:-

  • 97 and 98 are consecutive
  • They add up to 195:-
  • 97+98=195
  • [tex]\textbf{195=195}[/tex]
  • Since the LHS (left-hand side) equals the RHS (right-hand side), the integers are indeed 97 and 98.

Good luck.

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