The sum of the numerator and denominator of a fraction is 3 less than twice the denomiator.If the numerator and denomiator are decreased by 1,the numerator becomes half the denominator. Determine the fraction

See Related Questions below.

Ok

To solve this problem, let's start by assigning variables to the numerator and denominator of the fraction.

Let the numerator be represented by the variable 'n' and the denominator be represented by the variable 'd'.

According to the problem, the sum of the numerator and denominator is 3 less than twice the denominator. This can be written as the equation:

n + d = 2d - 3

Next, the problem states that if both the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Mathematically, this can be expressed as:

(n - 1) = (1/2)(d - 1)

Now we have a system of two equations. We can solve for the variables 'n' and 'd' by using any method of solving simultaneous equations, like substitution or elimination.

Let's use the method of substitution.

First, let's rearrange the first equation to express 'n' in terms of 'd':

n = 2d - 3 - d

Simplifying this, we get:

n = d - 3

Now, substitute this expression for 'n' in the second equation:

(d - 3 - 1) = (1/2)(d - 1)

Simplifying this, we get:

d - 4 = (1/2)(d - 1)

Multiply both sides of the equation by 2 to eliminate the fraction:

2(d - 4) = d - 1

Expand and simplify:

2d - 8 = d - 1

Move all terms with 'd' to one side and all constants to the other side:

2d - d = 1 - 8

d = -7

Since the denominator cannot be negative in this context, we discard this solution.

Therefore, there is no valid solution for the given system of equations, and we can conclude that there is no fraction that satisfies the given conditions.