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 𝑅 be equal to Robert’s games and 𝐻 be equal to Henry’s games. And then, we can say that 𝑅, the number of games Robert played, is equal to 𝐻, 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, that’s 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 𝑅 plus 𝐻 equals 34 and we know that 𝑅 equals 𝐻 plus 12, in our equation in place of 𝑅, we can substitute 𝐻 plus 12. And then, we have an equation that says 𝐻 plus 12 plus 𝐻 equals 34. We have two variables that are 𝐻. We can combine these like terms. 𝐻 plus 𝐻 equals two 𝐻. This is because when the coefficient of these variables are one, we just write the variable. So, one 𝐻 plus one 𝐻 equals two 𝐻. Two 𝐻 plus 12 is equal to 34.
We’re trying to solve for 𝐻 to find out how many games Henry played. So, we subtract 12 from both sides of the equation. Two 𝐻 plus 12 minus 12 equals two 𝐻. And 34 minus 12 equals 22. And then, we divide both sides by two. And we see that 𝐻 equals 11. If 𝐻 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 Robert’s games plus Henry’s 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.