The denominator of a fraction is 3 more than the numerator. If 5 is added to the numerator and 4 is subtracted from the denominator the value of the new fraction is 2. Find the original fraction?
n/(n+3)
(5 + n )/(n-1) = 2
5+n = 2 n - 2
n = 7
so
7/10
Anonymous subtracted 1 instead of 4 from the denominator.
repeat his steps using
(5 + n )/(n-4) = 2
Let's start by letting the numerator of the original fraction be represented by x.
According to the given information, the denominator is 3 more than the numerator, so we can represent it as (x + 3).
The original fraction can then be written as x/(x + 3).
Now, we are told that if 5 is added to the numerator and 4 is subtracted from the denominator, the value of the new fraction is 2.
So, the new numerator is (x + 5) and the new denominator is ((x + 3) - 4), which simplifies to (x - 1).
The new fraction can be written as (x + 5)/(x - 1).
We are given that this new fraction is equal to 2, so we can set up the following equation:
(x + 5)/(x - 1) = 2
To solve for x, we can start by cross-multiplying:
2(x - 1) = x + 5
Distributing on the left side:
2x - 2 = x + 5
Now, let's isolate the variable terms by subtracting x from both sides:
2x - x - 2 = 5
Simplifying:
x - 2 = 5
To solve for x, we'll add 2 to both sides:
x = 7
Therefore, in the original fraction, the numerator is 7 and the denominator is 7 + 3 = 10.
So, the original fraction is 7/10.
To solve this problem, let's consider the information given.
Let's say the numerator of the original fraction is represented by "x."
According to the problem, the denominator is 3 more than the numerator, so it can be represented as (x + 3).
The original fraction can then be written as x/(x + 3).
We are also given that when 5 is added to the numerator and 4 is subtracted from the denominator, the value of the new fraction is 2.
The new fraction can be written as (x + 5)/(x + 3 - 4), which simplifies to (x + 5)/(x - 1).
Now, we can set up an equation using the information given:
(x + 5)/(x - 1) = 2.
To solve for x, we can cross-multiply:
(x + 5) = 2(x - 1).
Expanding this equation gives:
x + 5 = 2x - 2.
Combining like terms, we have:
x - 2x = -2 - 5.
Simplifying further, we get:
-x = -7.
Finally, multiplying both sides of the equation by -1, we find:
x = 7.
So, the numerator of the original fraction is 7.
The denominator can be found by adding 3 to the numerator:
7 + 3 = 10.
Therefore, the original fraction is 7/10.