The sum of the numerator and denominator of a fraction is 17. If 3 is added to the numerator, the value of the fraction will be 1. What is the fraction?

1 answer

n = numerator

d = denominator

The sum of the numerator and denominator of a fraction is 17 mean:

n + d = 17

If 3 is added to the numerator, the value of the fraction will be 1 mean:

( n + 3 ) / d = 1

Now you have system of two equations:

n + d = 17

( n + 3 ) / d = 1

n + d = 17

Subtract d to both sides

n + d - d = 17 - d

n = 17 - d

( n + 3 ) / d = 1

Multiply both sides by d

n + 3 = d

Subtract 3 to both sides

n + 3 - 3 = d - 3

n = d - 3

n = n

17 - d = d - 3

Add d to both sides

17 - d + d = d - 3 + d

17 = 2 d - 3

Add 3 to both sides

17 + 3 = 2 d - 3 + 3

20 = 2 d

Divide both sides by 2

10 = d

d = 10

n = d - 3 = 10 - 3 = 7

Your fraction:

7 / 10

Proof:

n + d = 7 + 10 = 17

( n + 3 ) / d = ( 7 + 3 ) / 10 = 10 / 10 = 1