If the same integer is added to the numerator of the fraction 2/7 and subtracted from denominator, the fraction becomes 2. what is the integer?
Answers
Step-by-step explanation:
Solution :-
Let the required integer be X
Given fraction = 2/7
If X is added to the numerator then the fraction becomes (2+X)
If X is subtracted from the denominator then the fraction becomes (7-X)
Then the new fraction = (2+X)/(7-X)
According to the given problem
The new fraction = 2
=> (2+X)/(7-X) = 2
On applying cross multiplication then
=> 2+X = 2(7-X)
=> 2+X = 2×7 - 2×X
=> 2+X = 14-2X
=> X+2X = 14-2
=> 3X = 12
=> X = 12/3
=> X = 4
Therefore X = 4
Answer:-
The required integer for the given problem is 4
Check :-
The fraction = 2/7
If 4 is added to the numerator and 4 is subtracted from the denominator then the new fraction
=> (2+4)/(7-4)
=> 6/3
=> 2
We get the same result
Verified the given relations in the given problem.
Step-by-step explanation:
let the integer be x
2+x / 7-x = 2
2+x = 14 - 2x
2-14 = -2x - x
-12 = -3x
4= x