The denominator of a fraction is 2, more than twice the numerator. If 7 is added to both the numerator and the denominator the new fraction would be equivalent to 2/3. Determine fhe original fraction.

OK, so lets call the numerator n. The denominator is 7 more than twice the numerator. Put into an equation, it would look like this.

n/2n+7

You add 7 to both, and it will look like this:

n+7/2n+14

You should be able to solve from here.

Cheers!
Jeanne

Let's assume the numerator of the original fraction is x. According to the given information, the denominator of the original fraction is 2 more than twice the numerator, which means the denominator is 2x + 2.

The original fraction can be written as x/(2x + 2).

Now, if 7 is added to both the numerator and the denominator, the new fraction would be (x + 7)/(2x + 2 + 7), which is equivalent to 2/3.

So, we can set up the equation:

(x + 7)/(2x + 2 + 7) = 2/3

To solve for x, we can cross multiply:

3(x + 7) = 2(2x + 9)

3x + 21 = 4x + 18

Subtract 3x from both sides:

21 = x + 18

Subtract 18 from both sides:

3 = x

So, the numerator of the original fraction is 3.

Substituting this value into the original fraction (x/(2x + 2)), we get:

3/(2*3 + 2) = 3/8

Therefore, the original fraction is 3/8.

To solve this problem, let's assume that the numerator of the original fraction is "x".

According to the given information, the denominator is 2 more than twice the numerator. Thus, the denominator can be represented as 2x + 2.

Now, let's create our equation based on the information given:

(x + 7) / (2x + 2 + 7) = 2/3

Next, we can simplify the equation by multiplying both sides by the common denominator, which in this case is 3(2x + 9) since the denominators are different:
3(x + 7) = 2(2x + 9)

Expanding and simplifying, we have:
3x + 21 = 4x + 18

Bringing the variables together, we get:
3x - 4x = 18 - 21
-x = -3

Dividing both sides by -1, we find the value of x, which is:
x = 3

So, the numerator of the original fraction is 3.

To determine the denominator, we use the information given: the denominator is 2 more than twice the numerator. Plugging in x = 3 into this expression, we get:
2 * 3 + 2 = 8

Therefore, the original fraction is 3/8.

original: x/(2x+2)

now add 7 to both top and bottom. It is equal to 2/3.