The sum of one-third of a number and three-fourths of the number exceeds that number by one

x = 1/12

Step-by-step explanation:

x = a number

1/3x = one-third of a number

3/4x = three-fourths of the number

The sum of one-third of a number and three-fourths of the number exceeds that number by one

1/3x + 3/4x = x + 1

Convert the fractions so they have the same denominator.

Use a common factor - 12.

1/3x + 3/4x

4/4 (1/3) x + 3/3 (3/4) x = 4/12 + 9/12 = 13/12

13/12x = x + 1

Remove 1 from both sides to get x on it's own.

12/12 = 1

13/12 - 12/12 = x + 1 - 1

1/12 = x