math question involving algebra and fractions please help me!?

Question

the denominator of a fraction is four less than twice the nemerator.if three is added to both the numerator and denominator, the new fraction is equal to two thirds. find the original fraction. only an algebraic solution please!

Answer 1

Numerator would be x, denominator would be 2x - 4
When you add 3 to both, you end up with:
numerator = x+3, denominator = 2x -1

Set this up as a proportion: (x+3)/(2x-1) = 2/3
2(2x-1) = 3(x+3) ----- now u can solve it like a normal equation
4x - 2 = 3x + 9
x- 2 = 9
===> x=11
Plug in x=11 in your original fraction, you get 11/18

hope that helps!

Answer 2

"the denominator of a fraction is four less than twice the nemerator."
Let n be the numerator. Then the denominator is 2n - 4 and your existing fraction is

n / (2n - 4)

"if three is added to both the numerator and denominator, the new fraction is equal to two thirds."

In other words,

(n + 3) / [(2n - 4) + 3] = 2/3

Simplifying, we get (n + 3) / (2n - 1) = 2/3

We can now clear the denominators of the fractions by multiplying the entire equation through by a common denominator of the equation as a whole. In this case, multiplying by 3(2n - 1) does the trick. After the multiplication, our equation looks like

3(n + 3) = 2(2n - 1)

From here, you can solve for n, then use that value to find out what the original fraction n / (2n - 4) was.

Answer 3

Let the numerator be x
so denominator is 2x - 4

Original Fraction is x/(2x-4)
New Fraction (3+x)/(3+2x-4)
New Fraction = 2/3 so
2/3 = (3+x)/(3+2x-4)
2/3 = (3+x)/(2x-1)
(2x-1)*2/3 = (3+x)(2x-1)/(2x-1)
3*(2x-1)*2/3 = 3(3+x)
2(2x-1) = 3(3+x)
4x - 2 = 9 + 3x
4x - 3x - 2 = 9 + 3x - 3x
x -2 + 2 = 9 + 2
x = 11

Original Fraction = 11/18
New Fraction = 14/21

Answer 4

Let x the numerator
The fraction is x / 2x - 4
Adding 3 to both
(x + 3) / (2x - 1)
Then,
(x + 3) / (2x - 1) = 2/3
Solving this
x = 11
The original fraction is 11/18

Answer 5

let N = Numerator and let D = Denominator.

D = 2N -4 -------> call this eq1
(N+3)/(D+3) =2/3 -----------> call this eq2

2 equations with 2 unknowns.

From eq2 we get
N+3 = (2/3) (D +3)
N = (2/3) (D +3) -3 = 2D/3 +2 -3 = 2D/3 -1
from eq1 we have D = 2N -4 or N = D/2 +2

hence,
D/2 +2 = 2D/3 -1
D/2 -2D/3 = -3
-D/6 = -3
D =18

N = D/2 +2 = 9 +2 =11

Original fraction = N/D = 11/18

Answer 6

D = 2N - 4

(N + 3)/(D+3) = 2/3

3N + 9 = 2D + 6

3N + 3 = 2(2N-4) = 4N - 8
N = 11
D = 18

the fraction is 11/18


§

Answer 7

x/2x-4 is the original fraction
x+3/2x-1=2/3 is the second part
cross multiply
4x=3x+3
x=3

Answer 8

d+4=2n

d=2n-4

n+3/d+3=2/3

sub in d=2n-4 for d in second equation

n+3/(2n-4)+3=2/3

n+3/2n-1=2/3

4n-2=3n+9

n = 11

sub n=11 into first equation

d= 2(11)-4

d=18

Answer 9

x/2x-4

x+3/2x-1=2/3
lcd is 3(2x-1)
3(x+3)=2(2x-1)

3x+9=4x-2
11=x x+3 /2x-1= 14/21=2/3