In a game of tug-of-war, a team wins by pulling the flag over its goal line. the flag begins at 0. during a game, the flag moves 8 feet to the right, 12 feet to the left, and 13 feet back to the right. did a team win? explain

Think of the flag as 0 on a number line.  Move to the right is positive, move to the left is negative...

We begin on 0 and move 8 feet to the right. Now we move 12 feet to the left... 8 - 12 = -4.  We are at -4 on the number line.  Now we move back to the right 13 feet... -4 + 13 = 9.  We are at 9 on the number line.

So did any team win?  It depends on how far the goal line is from zero.  We know that it's farther than 8 feet from zero because they didn't call the game after the first 8 feet.  When it went back to the left it only went 4 feet from zero.  When it goes back to the right, it is now 9 feet from zero.  If the goal line is 9 feet or less from zero then one of the teams win... but if the goal line is greater than 9 feet from 0, no team wins (because nobody went that far).

Don't worry... I'm sure that both teams got a participation ribbon. . .

200,000+80,000+3,000+900+80+0. Hope it helps :)