SOLUTION: A fraction has a value of 3/4. If 4 is added to its numerator and 8 is subtracted to its denominator. The value of the resulting fraction is 1. What is the original fraction. Show

Question 1064373: A fraction has a value of 3/4. If 4 is added to its numerator and 8 is subtracted to its denominator. The value of the resulting fraction is 1. What is the original fraction. Show linear equation.
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x be the original numerator.
let y be the original denominator.

you get x/y = 3/4

when you add 4 to the numerator and subtract 8 from the denominator, you get:

(x + 4) / (y - 8) = 1

solve for x in the first equation to get x = 3/4 * y

replace x in the second equation with 3/4 * y to get:

(3/4 * y + 4) / (y - 8) = 1

multiply both sides of this equation to get:

3/4 * y + 4 = y - 8

subtract 4 from both sides of the equation to get:

3/4 * y = y - 12

subtract y from both sides of this equation to get:

-1/4 * y = -12

solve for y to get y = 48

go back to the original equation of x/y = 3/4 and replace y with 48 to get:

x/48 = 3/4

multiply both sides of this equation by 48 to get:

x = (3 * 48) / 4 = 3 * 12 = 36

you get x = 36 and y = 48

x/y = 36/48 = 3/4

(x+4) / (y-8) = (36+4) / (48-8) = 40/40 = 1

solution looks good.

the original fraction is 36/48.

Answer by MathTherapy(10555) (Show Source): You can put this solution on YOUR website!

A fraction has a value of 3/4. If 4 is added to its numerator and 8 is subtracted to its denominator. The value of the resulting fraction is 1. What is the original fraction. Show linear equation.

Let multiplicative factor be x
Then original fraction =
Adding 4 to the numerator, and subtracting 8 from the denominator results in:
4x - 8 = 3x + 4 ------- Cross-multiplying
4x - 3x = 4 + 8
x, or multiplicative factor = 12
Numerator: 3(12) or 36
Denominator: 4(12) or 48

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