Two-thirds of the way through the basketball season, Tina Thompson of the Houston Comets has an

Two-thirds of the way through the basketball season, Tina...

Key Concepts

Arithmetic Mean

The arithmetic mean, commonly known as the average, is calculated by summing a set of values and dividing by the number of values. It provides a central value that represents the data set and is widely used in various fields to summarize data with a single number.

Weighted Average

A weighted average takes into account the different sizes or weights of groups within the data. Instead of treating all groups equally, each group's average is multiplied by a factor reflecting its relative importance or size, and then combined to find the overall average. This concept is especially useful when different parts of the data contribute unequally to the final outcome.

Linear Equation

A linear equation is a mathematical statement that shows a relationship between variables using constants and coefficients without higher powers. In problems like this, forming and solving a linear equation allows us to find unknown values by establishing a balance between the total contributions of different parts of the data.

Proportional Reasoning

Proportional reasoning involves understanding how quantities scale relative to each other. In situations where parts of data sets or time periods have different averages or totals, proportional reasoning helps in setting up ratios or proportions that lead to the correct calculation of an unknown quantity.

Transcript

00:01 So two -thirds of the way through the season, tina thompson had averaged 18 points per game.

00:08 We want to determine how many more points she needs to average for the remaining of the season to have an average of 22 points by the end.

00:18 So it may help for us to think about this in terms of uniform rate, since we're talking about averages.

00:28 So we might look at d is equal to rt, just as we have an idea of.

00:33 Maybe where to start this problem at.

00:39 And i wrote the points per game for a very particular reason out like that, because notice that this looks a lot like miles per hour.

00:52 So maybe we can replace our rate with our average per game.

01:00 Our time instead is going to be the number of games played and distance will let's see if we do points per game times game the games cancel out and we're just left with points on the left side we'd have g all right so let's go ahead and see what we can work so by the end we want to average 22 points per game so let's just go ahead and plug that in so one equation will end up maybe needing to do something with is p is equal to 22 times game.

01:39 So we don't know how many games are played or how many points yet.

01:43 But let's actually write p as the following.

01:46 So p is going to be p1 plus p2, where p1 is the amount of points that she scored in the first two -thirds of the season, or the first two -thirds, and then for the last third is going to be p -2.

02:06 I'll just zoom out a little.

02:08 So so i'll write that right below as well.

02:13 So p1 is equal to two -third season points, and p -2 is equal to one -third, or last third, third of season points.

02:39 So let's see.

02:40 And actually, let me go ahead and get rid of this.

02:43 D is equal to r .t in the miles per hour, just so we're not looking and trying to figure out later on why we have those.

02:51 Right.

02:52 So let's start setting everything up.

02:55 So for the first third, or first two -thirds, she scored 18 points per game.

03:03 So this is going to be p1 is equal to.

03:07 So it's going to be 18 times...