[SOLVED] How many people standing in line?

Quote:

Originally Posted by fabxx

hey guys, this is on the OG Book section 6 #18
A group of people were standing single file in a line to buy movie tickets. As Juan stood in the line, he noticed that there were 9 more people behind him than there were in front of him. He also noticed that the total number of people in the line was 3 times the number of people in front of him. How many people were in the line?

The correct answer is 30.
I didn't get 30 but below is my work. Please kindly tell me where i got wrong. Thanks in advanced

we know there's 9 people in front and also 9 people behind him so plus Juan there's 19 people. There's 3 times the number of people in front of him so therefore 27 +9+1=37. But how come the correct answer is 30?

Thanks in advance!!

Let the number in front be x.

Then number of people behind is x + 9.

Therefore number of people in line is x + (x + 9) + 1. The 1 is obviously Juan himself.

Therefore x + (x + 9) + 1 = 3x => 2x + 10 = 3x => x = 10.

Therefore number of people in line is x + (x + 9) + 1 = 30.