Find the original number.

Question

The denominator of a rational no. is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to its denominator, the new no. becomes 1/5. What is the original number?

 

 

Answer 1

Hi Lavanya, let n represent the original numerator. Then n + 3 represents the original denominator.

 

Now, subtract 3 from the original numerator, or n - 3, and add 2 to the original denominator, or (n + 3) + 2.

 

The new numerator, n - 3, divided by the new denominator, n + 5, must equal 1 / 5.

 

Set up:

 

(n - 3) / (n + 5) = 1 / 5

 

Cross multiplying gives:

 

5 * (n - 3) = n + 5

 

5n - 15 = n + 5

 

Add 15 to both sides:

 

5n = n + 20

 

Subtract n from both sides:

 

4n = 20

 

Divide both sides by 4:

 

n = 5

 

The original numerator is 5.

 

Check:

 

Substitue for n:

 

5 / (5 + 3), 5 / 8

 

Subtract 3 from 5 and add 2 to 8:

 

(5 - 3) / (8 + 2)

 

2 / 10 = 1 / 5

 

Values check.

 

Questions?