How many points did the​ team's defense give up in the third football​ game?

Question

After playing two football​ games, a professional football​ team's defense had given up an average of 28 points per game.

After playing a third football​ game, the​ team's defense had given up an average of 23 points per game.

How many points did the​ team's defense give up in the third football​ game?

Answer 1

Let Xi be the points allowed per game. You know the following:

(X1 + X 2) / 2 = 28

(X1 + X2 + X3) / 3 = 23

Solving for X1 + X2 in the first equation yields X1 + X2 = 56

Substituting that into the second equation yields (56 + X3) / 3 = 23, or 56 + X3 = 69, thus X3 = 13.