A number, half of that number, and one fifth of that number are added. The result is 51. What is the original number?

Let the original number be ‘x’

Then half of that number = 1/2x or simply x/2

Similarly one fifth of that number = x/5

According to the question

x+x/2+x/5=51

Taking LCM

10x/10+2x/10+5x/10=51

Multiplying 10 throughout

10x+2x+5x=510

17x=510

x=510/17

Therefore x=30