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Sagot :
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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