### Video Transcript

In a football league season, Robert played 12 games more than Henry. If they played a total of 34 games combined, how many games did Henry play?

We can let ๐
be equal to Robertโs games and ๐ป be equal to Henryโs games. And then, we can say that ๐
, the number of games Robert played, is equal to ๐ป, the number of games Henry played, plus 12. This is because Robert played 12 games more than Henry. So, if we take the number of games Henry played and add 12, thatโs the number of games Robert played. We also know that, combined, they played 34 games. So, the number of games Robert played plus the number of games Henry played equals 34.

If we know that ๐
plus ๐ป equals 34 and we know that ๐
equals ๐ป plus 12, in our equation in place of ๐
, we can substitute ๐ป plus 12. And then, we have an equation that says ๐ป plus 12 plus ๐ป equals 34. We have two variables that are ๐ป. We can combine these like terms. ๐ป plus ๐ป equals two ๐ป. This is because when the coefficient of these variables are one, we just write the variable. So, one ๐ป plus one ๐ป equals two ๐ป. Two ๐ป plus 12 is equal to 34.

Weโre trying to solve for ๐ป to find out how many games Henry played. So, we subtract 12 from both sides of the equation. Two ๐ป plus 12 minus 12 equals two ๐ป. And 34 minus 12 equals 22. And then, we divide both sides by two. And we see that ๐ป equals 11. If ๐ป equals 11, we can say that Henry played 11 games. This solves our question.

But if we were interested in how many games Robert played or if we wanted to check our work, we know that Robert played 12 more games than Henry. If Henry played 11 games, then Robert played 11 plus 12. Robert played 23 games. And to check our work, we can say, do Robertโs games plus Henryโs games total to 34? Does 23 plus 11 equal 34? It does. And so, we know that Robert played 23 games and Henry played 11 games.