Question

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

Answer 1

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`\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}`

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

`\blue{\textsf{\textbf{\underline{\underline{Answer:-}}}}`

The integers are 97 and 98.

`\blue{\textsf{\textbf{\underline{\underline{How to Solve:-}}}}`

If integers are
`\textbf{consecutive,}` 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:-

`\bigstar{\fbox{n+n+1=195}`

`\textsf{\underline}}`Add the n's:-

`\Longrightarrow`
`\sf{2n+1=195}`

Subtract 1 on both sides:

`\sf{2n=195-1}`

`\sf{2n=194}`

Divide by 2 on both sides:-

`\bigstar{\fbox{n=97}`

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
• 
  `\textbf{195=195}`
• 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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Answer 2

Hey ! there

Answer:

• First Integer is 97

• Second Integer is 98

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 ,

`\dashrightarrow \qquad \: x + x + 1 = 195`

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

`\dashrightarrow \qquad \: 2x + 1 = 195`

Step 2 : Subtracting 1 on both sides :

`\dashrightarrow \qquad \: 2x + \cancel{1} - \cancel{1} = 195 - 1`

Simplifying it ,

`\dashrightarrow \qquad \: 2x = 194`

Step 3 : Dividing with 2 on both sides :

`\dashrightarrow \qquad \: \frac{ \cancel{2}x}{ \cancel{ 2}} = \cancel{(194)/(2) }`

On further calculations , We get :

`\dashrightarrow \qquad \: \purple{\underline{\boxed{\frak{ x = 97}}}} \quad \: \bigstar`

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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