Find a number that is 58 more than the sum of its third, tenth, and twelfth parts.
Let x represent the number:
x/3 + x/10 + x/12 + 58 = x.
Least common denominator is 60.
60x/3 + 60x/10 + 60x/12 + 58·60 = 60x.
20x + 6x + 5x + 3480 = 60x.
29x = 3480.
x = 120.
Least common denominator is 60.
60x/3 + 60x/10 + 60x/12 + 58·60 = 60x.
20x + 6x + 5x + 3480 = 60x.
29x = 3480.
x = 120.
Check: 120 = 58 + 40 + 12 + 10.