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
