The denominator of a fraction is greater than its numerator by 3. if 3 is subtracted from the numerator and 2 is add to the denominator, the new fraction is 1/5. the sum of the numerator and the denominator of the original fraction is
Answers
Answer:
The sum of the numerator and the denominator of the original fraction is 13.
Step-by-step explanation:
Given :
The denominator of a fraction is greater than its numerator by 3.
If 3 is subtracted from the numerator and 2 is added to the denominator, the new fraction is 1/5.
To find :
Sum of the numerator and the denominator of the original fraction.
Solution :
Consider,
Numerator of the fraction = x
★ The denominator of the fraction is greater than its numerator by 3.
Then,
Denominator of the fraction = (x+3)
★ If 3 is subtracted from the numerator and 2 is added to the denominator, the new fraction is 1/5.
According to the question :-
\to \sf \: \dfrac{x - 3}{x + 3 + 2} = \dfrac{1}{5}→
x+3+2
x−3
=
5
1
\to \sf \: \dfrac{x - 3}{x + 5} = \dfrac{1}{5}→
x+5
x−3
=
5
1
\to \sf \: 5x - 15 = x + 5→5x−15=x+5
\to \sf \: 5x - x = 5 + 15→5x−x=5+15
\to \sf \: 4x = 20→4x=20
\to \sf \: x = \dfrac{20}{4}→x=
4
20
\to \sf \:x = 5→x=5
Numerator = 5
Then,
Denominator = (5+3) = 8
Therefore,
The sum of the numerator and the denominator of the original fraction,
= 5 + 8
= 13