The denominator of a fraction is 4 more than the numerator. If both the numerator and the denominator of a fraction are increased by 1, the resulting fraction equals 1/2. Find the fraction.
Answers
Given : The denominator of a fraction is 4 more than the numerator. If both the numerator and the denominator of a fraction are increased by 1, the resulting fraction equals 1/2
To Find : the fraction.
Solution:
Let say that Fraction is p/q
Numerator = p
denominator = q
The denominator of a fraction is 4 more than the numerator.
=> q = p + 4
Hence Fraction is p/(p + 4)
both the numerator and the denominator of a fraction are increased by 1
=> (p + 1)/(p + 4 + 1) = 1/2
=> (p + 1)/(p + 5) = 1/2
=> 2p + 2 = p + 5
=> p = 3
Fraction is 3/(3 + 4)
= 3/7
fraction. is 3/7
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Answer:
The fraction is 3/7.
Step-by-step explanation:
Suppose numerator is x
And denominator is y.
The fraction is x/y
By first condition,
y = x + 4 ........ (1)
By second condition,
(x + 1)/(y + 1) = 1/2
=> 2 * (x + 1) = 1 * (y + 1)
=> 2x + 2 = y + 1
=> 2x + 2 = x + 4 + 1 ...... (From 1)
=> 2x + 2 = x + 5
=> 2x - x = 5 - 2
=> x = 3
Put x = 3 in eqn (1)
y = x + 4
=> y = 3 + 4
=> y = 7
So,
The fraction is 3/7.