Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

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

Sagot :

TheAmethyst

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 .

#Keep Learning

           - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

[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.

            - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.