The value of the numerator of a particular fraction is one-half the value of its denominator. If the numerator is increased by 2

Question

3 years ago

8

and the denominator is decreased by 2, the value of the resulting fraction is 3/4. What is the denominator of the original fraction? URGENT!

1 answer:

IgorC [24] · Answer 1 · 2022-07-13T19:25:34+03:00

Answer:

14

Step-by-step explanation:

Let the original denominator be 2x.

The original numerator is x.

The original fraction is x/(2x).

The numerator is increased by 2, and the denominator is decreased by 2.

The new fraction is (x + 2)/(2x - 2).

The new fraction equals 3/4.

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

Cross multiply.

4(x + 2) = 3(2x - 2)

4x + 8 = 6x - 6

-2x = -14

x = 7

The original numerator was 7.

2x = 2(7) = 14

The original denominator was 14.