Video Transcript
In a soccer tournament, a team
scored 32 goals with a mean of two goals per game. How many games did they play in
total?
We’ve been told the total number of
goals scored by the team and the mean, or average, number of goals they scored per
game. We can recall that the mean of a
data set is calculated by dividing the sum of all the values in the data set by how
many values there are. In this example, in which we’re
interested in the mean number of goals scored per game, this corresponds to dividing
the total number of goals scored by the team during the tournament by the number of
games they played.
We’re given that the mean number of
goals scored per game was two and that the total number of goals the team scored was
32. We don’t know the number of games
played, and it’s this we need to calculate. Substituting the values we do know
and using 𝑛 to represent the number of games played gives the equation two equals
32 over 𝑛. We can solve this equation in two
ways.
The more formal approach is to
first multiply both sides of the equation by 𝑛, leading to two 𝑛 equals 32. We can then divide both sides of
the equation by two to give 𝑛 equals 16. The less formal approach would
simply be to ask ourselves, 32 divided by what equals two? And of course, we should recall
that 32 is twice 16, so 32 divided by 16 is two.
We’ve therefore found that the team
played 16 games in total during the tournament.
