If a certain number is added to both the numerator and denominator of a given fraction, its value is 1/2 . However, if the same number is subtracted from both the numerator and denominator, its value is 1/7 . If, however, 1 is added to both numerator and denominator, the fraction is 2/5 . Find the fraction.
Answers
Answer:
sorry I can't find because I am on 3rd grade
Given : If a certain number is added to both the numerator and denominator of a given fraction, its value is 1/2 .
However, if the same number is subtracted from both the numerator and denominator, its value is 1/7 .
If, however, 1 is added to both numerator and denominator, the fraction is 2/5 .
To Find : the fraction.
Solution:
Fraction = N/D
N = numerator
D = denominator
(N + 1)/(D + 1) = 2/5
=> 5N + 5 = 2D + 2
=> 5N + 3 = 2D
Certain Number Added = x
(N + x)/(D + x) = 1/2
=> 2N + 2x = D + x
=> 2N + x = D
=> x = D - 2N
(N - x)/(D - x) = 1/7
=> 7N -7x = D - x
=> 7N - D = 6x
=> 7N - D = 6(D - 2N)
=> 7N - D = 6D - 12N
=> 19N = 7D
=> 19N = 7(5N + 3)/2
=> 38N = 35N + 21
=> 3N = 21
=> N = 7
19 (7) = 7(D)
=> D = 19
Fraction is 7/19
Additional Info :
On solving x = 5
7/19 = (7 + 1)/(19 + 1) = 8/20 = 2/5
(7 + 5)/(19 + 5) = 12/24 = 1/2
(7 - 5)/(19 - 5) = 2/14 = 1/7
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