the numerator of a fraction is 3 less than the numerator.If half of the numerator is added to the numerator and the denominator,the resulting fraction is 1/2.Find the the fraction.
It would help if you proofread your questions before you posted them.
"the numerator of a fraction is 3 less than the numerator"?
To solve this problem, let's first break down the information given.
Let's call the numerator of the fraction 'x' and the denominator 'y'.
According to the problem, the numerator is 3 less than the numerator, which can be written as:
x = x - 3
Next, it states that if half of the numerator is added to the numerator and the denominator, the resulting fraction is 1/2. This can be expressed as:
(x + (x/2)) / (y + (x/2)) = 1/2
Let's simplifly this equation further:
[(2x + x) / 2] / [(y + (x/2))] = 1/2
(3x / 2) / (y + (x/2)) = 1/2
Now we can set up an equation using the first piece of information:
x = x - 3
Substituting this into the second equation:
(3x / 2) / (y + (x/2)) = 1/2
(3(x - 3) / 2) / (y + ((x - 3)/2)) = 1/2
Simplifying further:
(3x - 9) / 2 / (y + ((x - 3)/2)) = 1/2
(3x - 9) / 2 = (y + ((x - 3)/2)) / 2
2(3x - 9) = y + (x - 3)
6x - 18 = y + x - 3
5x - y = 15
Now we have a system of equations:
x = x - 3
5x - y = 15
To solve this system, we can substitute the first equation into the second:
5(x - 3) - y = 15
5x - 15 - y = 15
5x - y = 30
Now we have a new equation:
5x - y = 30
Comparing it to the equation from earlier:
5x - y = 15
We notice that the equation is the same, just with different constants. Therefore, there is no unique solution to this system of equations.
This means that there is no solution for the given conditions.