The numerator of a certain fraction is four times the denominator. If 6 is added to both the numerator and the denominator, the resutling fraction is equivalent to 2. What was the original fraction ?

Let's start by representing the original fraction as x/y, where x is the numerator and y is the denominator.

According to the given information, the numerator is four times the denominator. So we can write the equation:

x = 4y

Next, we are told that if 6 is added to both the numerator and the denominator, the resulting fraction is equivalent to 2. This can be written as another equation:

(x + 6) / (y + 6) = 2

Now we have two equations:

x = 4y (equation 1)
(x + 6) / (y + 6) = 2 (equation 2)

To solve this system of equations, we can substitute the value of x from equation 1 into equation 2:

(4y + 6) / (y + 6) = 2

To simplify, we can cross-multiply:

4y + 6 = 2(y + 6)

Expanding the equation:

4y + 6 = 2y + 12

Combining like terms:

4y - 2y = 12 - 6

2y = 6

Dividing both sides by 2:

y = 3

Now that we have the value of y, we can substitute it back into equation 1 to find x:

x = 4y
x = 4(3)
x = 12

Therefore, the original fraction is 12/3.

To solve this problem, let's break it down step by step:

Let's assume the denominator of the original fraction is x.

According to the problem, the numerator is four times the denominator. Therefore, the numerator would be 4x.

We're also given that if 6 is added to both the numerator and denominator, the resulting fraction is equivalent to 2.

So, the new numerator would be 4x + 6, and the new denominator would be x + 6.

To find the original fraction, we need to set up an equation using the new numerator and denominator:

(4x + 6) / (x + 6) = 2

To solve for x, we can cross-multiply:

2(x + 6) = 4x + 6

Distribute 2 on the left side:

2x + 12 = 4x + 6

Subtract 2x from both sides to get the x terms on one side:

12 = 2x + 6

Subtract 6 from both sides:

6 = 2x

Divide both sides by 2:

x = 3

Now we know the original denominator is 3.

To find the original numerator, we can substitute the value of x into our previous equation:

Numerator = 4 * denominator = 4 * 3 = 12

Therefore, the original fraction is 12/3, which simplifies to 4/1 or just 4.

original fraction is 4x/x, clearly not in lowest terms of 4

solve (4x+6)/(x+6) = 2
I get x = 3

so the original fraction was 12/3, which of course should have been reduced to 4.

(I really don't like this question, sloppy planning mathematically.)

4d=n

4y=x
x+6/y+6=2