A basketball player averaged 20 points a game over the course of six games. His scores in five of those games were 23, 18, 16, 24, and 27. How many points did he score in the sixth game?

Question

heisenberg · Answer

So this is a basic algebra problem. Using your knowledge for averages and treating any unknown values as variables, let's take look:

heisenberg · Answer

the average of n numbers: (n1 + n2 + n3 + ... nn) / n
ie:
$$\frac{\sum_{i=1}^{n}n_i}{n}$$

heisenberg · Answer

that notation may be a little advanced. it just says the sum of all the numbers divided by the number of numbers. so we can carry on, treating unknowns as variables and then attempting to solve:

heisenberg · Answer

$$\frac{(23 + 18 + 16 + 24 + 27 + x)}{6} = 20$$
now we solve for x

heisenberg · Answer

108 + x = 20 * 6

heisenberg · Answer

x = 120 - 108 = 12.

heisenberg · Answer

so we know in his 6th game he scored 12 points.

anonymous · Answer

Thank you, but how did you know to subtract? do you do the opposite when you flip the equation over

heisenberg · Answer

yes, when dealing with an equation, if you do one thing to one side of the equation, you must do the same to the other side.

Since we had
108 + x = 20 * 6
we want to just have x on the left side, so we subtract 108 from each side.
108 + x - 108 = 20 * 6 - 108
the 108s on the left cancel, like we wanted.

anonymous · Answer

thank you so much,