The sum of numerator and denominator
of a
centain fraction is 8. If 2 is
added to the numerator and to the denominator,
the value
of the fraction is
increased by 4/35. Find the fraction.
Answers
Answer:
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.
\frac{x+2}{y+2} = \frac{x}{y} + \frac{4}{35}
\frac{x+2}{8 - x+2} = \frac{x}{8 - x} + \frac{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.
Hope the helps!
Answer:
Step-by-step explanation:
Solution :-
Let the numerator be x and the denominator be y.
Fraction = x/y.
According to the Question,
1st Part,
⇒ x + y = 8
⇒ x = 8 - y .......(i)
2nd Part,
⇒ (x + 2)/(y + 2) = x/y + 4/35
Putting x's value, we get
⇒ (8 - y + 2)/(y + 2) = (8 - y)/y + 4/35
⇒ (10 - y)/(y + 2) = 35(8 - y) + 4y/35y
⇒ 35y(10 - y) = (y + 2) (280 - 31y)
⇒ - 35y² + 31y² + 350y - 280y + 62y - 560 = 0
⇒ y² - 33y + 140 = 0
⇒ y² - 28y - 5y + 140 = 0
⇒ y(y - 28) - 5(y - 28) = 0
⇒ (y - 28) (y - 5) = 0
⇒ y = 28 or y = 5
Putting y's value in Eq (i), we get
⇒ x = 8 - y or 8 - y
⇒ x = 8 - 28 or 8 - 5
⇒ x = - 20 or 3 (Neglecting negative value one)
⇒ x = 5
So, x = 3 and y = 5
Hence, the required fraction is 3/5.
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