The denominator of a fraction is four more than twice the numerator. If both numerator and denominator are increased by six, the simplified result is 7/13. Find the original fraction

original fraction: n/(2n+4)

modified fraction:
(n+6)/(2n+4+6) = 7/13
13(n+6) = 7(2n+10)
13n+78 = 14n+70
-n = -8
n=8

So, the original fraction was 8/20
and the new value is 14/26 = 7/13

Why did the math book go to the comedy club? Because it wanted to find some good material for its fractions!

Let's tackle this problem together. Let's call the numerator "n" and the denominator "d".

According to the problem, the denominator is four more than twice the numerator, so we can write the equation:

d = 2n + 4

Now, if both the numerator and the denominator are increased by six, we get:

(n + 6)/(d + 6) = 7/13

But we also know that d = 2n + 4, so we can substitute it into the equation as:

(n + 6)/(2n + 4 + 6) = 7/13

Simplifying this equation, we have:

(n + 6)/(2n + 10) = 7/13

To get rid of the fractions, we can cross-multiply:

13(n + 6) = 7(2n + 10)

Simplifying further:

13n + 78 = 14n + 70

Rearranging terms:

14n - 13n = 78 - 70

n = 8

Now, we can substitute the value of n into the equation d = 2n + 4:

d = 2(8) + 4
d = 16 + 4
d = 20

So the original fraction is 8/20, which can be simplified to 2/5.

Hope that brings a fraction of humor to your day!

Let's begin by assigning variables to the numerator and denominator of the fraction. Let's say the numerator is represented by "x" and the denominator is represented by "y."

According to the given information, we can set up two equations:

1) "The denominator of a fraction is four more than twice the numerator."
This can be expressed as: y = 2x + 4.

2) "If both numerator and denominator are increased by six, the simplified result is 7/13."
After increasing numerator and denominator by six, the new fraction is (x + 6)/(y + 6).
Since this fraction is simplified and equivalent to 7/13, we can write the equation: (x + 6)/(y + 6) = 7/13.

To solve this system of equations, we can substitute the value of y from the first equation into the second equation:

(x + 6)/(2x + 4 + 6) = 7/13.
Simplifying the second equation, we have:

(x + 6)/(2x + 10) = 7/13.

Now, we can cross multiply:

13(x + 6) = 7(2x + 10).

Expanding the equation:

13x + 78 = 14x + 70.

Moving all terms to one side:

13x - 14x = 70 - 78,
-x = -8.

Finally, dividing by -1:

x = 8.

Now, we can substitute the value of x (which is 8) back into the first equation to find y:

y = 2x + 4,
y = 2(8) + 4,
y = 16 + 4,
y = 20.

Therefore, the original fraction is 8/20.

To solve this problem, let's assign variables to the unknowns. Let's call the numerator of the fraction 'x' and the denominator of the fraction 'y.'

According to the problem, the denominator is four more than twice the numerator. So, we can write the equation as:

y = 2x + 4

Next, it says that if we increase both the numerator and denominator by six and simplify the result, we get 7/13. Mathematically, this can be represented as:

(x + 6) / (y + 6) = 7/13

Now, we have a system of two equations:

1. y = 2x + 4
2. (x + 6) / (y + 6) = 7/13

We can solve this system of equations using substitution or elimination methods. Let's use the substitution method in this case.

From the first equation, we can rewrite it as:

x = (y - 4)/2

Now, substitute this value of x into the second equation:

[(y - 4)/2 + 6] / (y + 6) = 7/13

Now, cross multiply to get:

13(y - 4 + 12) = 2(y + 6) * 7

Simplify the equation:

13(y + 8) = 14(y + 6)

Expand the equation:

13y + 104 = 14y + 84

Rearrange and simplify:

14y - 13y = 104 - 84

y = 20

Now, substitute the value of y back into the first equation:

x = (20 - 4)/2

x = 8

Therefore, the original fraction is 8/20, which can be simplified to 2/5.