Question

Amanda has scored 24,22,27,23 and 30 points in her five basketball games so far. How many points does she need to score in her next game so that her average (mean) is 25 points per game?

Answer 1

To answer this question, we need to remember that the mean of a data is the sum of the data divided by the total number of elements that represent this data.

Therefore, if we need to find the sixth value for which the average (mean) per game is 25 points, we can proceed as follows:

`(24+22+27+23+30+x)/(6)=25`

Now, to find the value, x, we need to follow the next steps:

1. Add the values in the numerator of the fraction:

`(126+x)/(6)=25`

2. Multiply both sides by 6:

`\begin{gathered} (6\left(126+x\right?)/(6)=6\left(25\right? \\ (6)/(6)\left(126+x\right?=150 \\ 126+x=150 \end{gathered}`

3. Finally, subtract 126 from both sides of the equation:

`\begin{gathered} 126-126+x=150-126 \\ x=24 \end{gathered}`

Therefore, the value she needs is 24 points.

And we can check this value as follows:

`(24+22+27+23+30+24)/(6)=(150)/(6)=25`

Therefore, in summary, we have that Amanda needs to score 24 points in the next game so that her average is 25 points per game.