One seventh of a number added to one third of the same number is 67 . find the number. express your answer as a fraction in simplest form.

Say the number equals x.

Then:

one seventh of a number:

1/7x

one third of the same number:

1/3x

Added to each other:

1/7x + 1/3x 

equals 67:

1/7x + 1/3x = 67

Then what you can do is add the two fractions together. To do this, convert the denominators to 21.

1/7x * 3/3 + 1/3x * 7/7 = 67

3/21x + 7/21x = 67

10/21x = 67

Then divide everything by 10/21.

10/21x = 67

/(10/21)   /(10/21)

Which is basically the same as multiplying by the reciprocal of the divisor.

x = 67 * 21/10

x = 1407/10