The sum of the numerator and denominator of a certain fraction is 11. If 1 is added to both numerator and denominator the fraction increases by 3/56. Find the fraction. Detailed answer plz.....
Answers
Step-by-step explanation:
Let the numerator be x and denominator be y.
The fraction is x/y.
Given that their sum = 8.
x + y = 8 ------ (1)
y = 8 - x --------- (2)
Given that if 2 is added to both numerator and denominator, the fraction is increased by 4/35.


35(x + 2)(8-x) = 35x(10-x)+4(8-x)(10-x)
-35x^2 +210x + 560 = -31x^2 +278x + 320
-35x^2 -68x +240=-31x^2
-4x^2 -68x + 240 = 0
x^2 + 17x -60=0
x^2 - 3x +20x - 60 = 0
x(x - 3) + 20(x - 3) = 0
x = 3 (or) x = -20.
Since x cannot be -ve, so x = 3.
Then y = 8 - x
= 8 - 3
= 5.
Therefore the fraction = 3/5.
This is the similar eg. do it by taking the help of this
Answer:
103/109
Step-by-step explanation:
let number be n/d
n+d=2
n+1/d+1=n/d+3/56
n+1/d+1=56n+3/56d
cross multiply
56d(n+1)=(d+1)(56n+3)
56nd+56d=56nd+56n+3d+3
56nd-56nd+56d-56n-3d=3
53d-56n=3------------1
53d+53n=106--------2
2-1
106n=103
n=103/106
then d =2-103/106
=109/106
number is n/d
= 103/106 ÷109/106
=103/109
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