1. If 2 is added to both the numerator and
denominator of a rational number its value
becomes double. If 8 is added to both the
numerator and denominator its value becomes
triple. Find the number.
Answers
Answered by
1
Answer:
1/4
Step-by-step explanation:
Let numerator be equal to x and denominator be equal to y.
Then, x/y would represent the fraction.
So, (x+2)/(y+2) = 2x/y
xy + 2y = 2xy + 4x
2y = xy + 4x (1)
Also, (x+8)/(y+8) = 3x/y
xy + 8y = 3xy + 24x
8y = 2xy + 24x
4y = xy + 12x (2)
Subtracting 1 and 2.
2y = 8x
y = 4x
Substituting this back in 1
2(4x) = x(4x) + 4x
8x = 4x^2 + 4x
4x = 4x^2
x = 1 or x = 0
Since, x can't be equal to 0, so x =1
y = 4(1) = 4
So, fraction= 1/4
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