in a rational number, twice the numerator is two more than the denominator. if we add 3 to each, the new fractions is 2/3. find the original fraction.
Answers
Answer:
Step-by-step explanation:
Let’s use x as the numerator, and I’ll explain everything else in terms of x.
From what you are describing, the equation would be (x+3)/(2x+1)=2/3.
I got here firstly by creating the “original fraction, which consists of a numerator x, and a denominator 2x - 2 (two less than twice the numerator). I then added 3 to both the numerator and denominator, and then I simplified them. I then equated this all to 2/3, the fraction you wanted them to equal.
Now, let’s solve this out. We can cross multiply:
(x+3) * 3 = (2x+1) * 2
Now, let’s distribute the 3 and 2:
3x + 9 = 4x + 2
3x + 7 = 4x
-3x -3x
7 = 1x
x=7
Therefore, the original fraction is 7/12.
7/12 add 3 to both the numerator and denominator becomes 10/15, which is 2/3.