the sum of the numerator and denominator of a certain 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:
4 and for explaination
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Answer:
3/5
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.
\frac{x+2}{y+2} = \frac{x}{y} + \frac{4}{35}
y+2
x+2
=
y
x
+
35
4
\frac{x+2}{8 - x+2} = \frac{x}{8 - x} + \frac{4}{35}
8−x+2
x+2
=
8−x
x
+
35
4
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.