Question

The denominator of a rational number is greater than its numerator by 7. If the numerator is increased by 19 and the denominator is decreased by 3, the new number becomes 4. Find the original number. please explain step by step.​

Answer 1

Answer :

• The Original number is 1/8

Given :

• The denominator of a rational number is greater than its numerator by 7
• If the numerator is increased by 19 and the denominator is decreased by 3 , the new number becomes 4

To find :

• The original number

Solution :

• Let the numerator be x

Given that, the denominator of a rational number is greater than its numerator by 7 so,

• Denominator be x + 7

Then, Original number will be x/x + 7

According to question :

The numerator is increased by 19 and the denominator is decreased by 3 , the new number becomes 4 so,

➞ x + 19/x + 7 - 3 = 4

➞ x + 19/x + 4 = 4

➞ 4(x + 4) = x + 19

➞ 4x + 16 = x + 19

➞ 4x - x = 19 - 16

➞ 3x = 3

➞ x = 3/3

➞ x = 1

Finding the original number :

➞ x/x + 7

➞ 1/1 + 7

➞ 1/8

Hence,The Original number is 1/8

Verification :

➞ x + 19/x + 7 - 3 = 4

➞ 1 + 19/1 + 7 - 3 = 4

➞ 20/1 + 4 = 4

➞ 20/5 = 4

➞ 4 = 4

Hence , Verified