Question

The numerator of a fraction it 5 less than it's denominator. If 6 is added to the numerator and 4 to the denominator, the fraction is double. What is the fraction

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let x be the denominator of the fraction.

The numerator is x - 5.
After adding 6 to the numerator and 4 to the denominator, the new fraction becomes (x - 5 + 6)/(x + 4) = (x + 1)/(x + 4).
According to the problem, (x + 1)/(x + 4) = 2(x/(x + 4)).
Simplifying the equation, we get x + 1 = 2x.
Subtracting x from both sides of the equation, we get 1 = x.
Therefore, the denominator of the fraction is 1.
The numerator is 1 - 5 = -4.
So, the fraction is -4/1, which is equivalent to -4. Answer: \boxed{-4}.

Answer 2

[AI-generated answer — Step-by-Step Bot]

Let's assume the denominator of the fraction as "x".

According to the given information, the numerator of the fraction is 5 less than its denominator, which can be represented as (x - 5).

If we add 6 to the numerator and 4 to the denominator, the new fraction is double the original fraction.

So, the equation can be written as:
(2/1) * (x - 5) = (x + 4 + 6)

Now, let's solve the equation step-by-step to find the value of x.

First, simplify the equation:
2(x - 5) = x + 10

Expanding the equation:
2x - 10 = x + 10

Moving the constants to one side and variables to the other side:
2x - x = 10 + 10
x = 20

Therefore, the denominator of the fraction is 20.

Now, we can substitute the value of x in the equation (x - 5) to find the numerator:
Numerator = 20 - 5 = 15

Hence, the fraction is 15/20 or simplified as 3/4.

Answer 3

[AI-generated answer — Explain Bot]

To find the fraction, let's assign variables to the numerator and denominator. Let's say the numerator is represented by "x" and the denominator is represented by "y".

According to the problem, the numerator is 5 less than the denominator, so we can form an equation: x = y - 5.

Additionally, if we add 6 to the numerator and 4 to the denominator, the resulting fraction is double. We can now write another equation: (x + 6) / (y + 4) = 2.

Now that we have two equations, we can solve them simultaneously to find the values of x and y.

From the first equation, x = y - 5, we can substitute this relationship into the second equation:

((y - 5) + 6) / (y + 4) = 2.

Simplifying this equation, we get: (y + 1) / (y + 4) = 2.

We can now cross-multiply to solve for y:

y + 1 = 2(y + 4),
y + 1 = 2y + 8,
y - 2y = 8 - 1,
-y = 7.

Multiplying both sides of the equation by -1 to solve for y, we get y = -7.

Now that we have the value for y, we can substitute it back into the first equation to find x:

x = y - 5 = -7 - 5 = -12.

Therefore, the fraction is -12/-7. However, we can simplify it by dividing both numerator and denominator by their greatest common divisor, which is 1. So the final simplified fraction is:

12/7.

Hence, the fraction is 12/7.