Step-by-step explanation:
I guess, the problem is to understand :
what means "average" ?
well, the average of a defined set of data points is the sum of the data divided by the number of data points (or samples).
that way you get a mean value for each time the system is "measured" (a data point is created).
each new measurement / data point changes the mean value (or average).
this is used all the time - in sports statistics (e.g. the average score of a team), in daily life (like the average height of a human being that defines sizes of clothes, beds, chairs, tables, even the typical height of ceilings and so on).
the average of these 8 data points is therefore :
(36+37+34+23+47+27+31+21)/8 = 256/8 = 32
so, if he wants to raise his average score to 35 with the results of the next 2 games, this has 2 things to be considered :
1. the number of days points will be then 8+2=10 (and not just 8).
2. we need to add 2 data points, so that the sum of all 10 data points divided by 10 is then 35.
(36+37+34+23+47+27+31+21+x+y)/10 = 35
(36+37+34+23+47+27+31+21+x+y) = 350
x + y = 350 - 256 = 94
that means, he has to score a total of 94 points in the next 2 games.
it does not matter, how many in any single game, as long as the sum of both games is 94.
since the question is phrased "how many in each of the next 2 games", we simply take the target average of these 2 games.
remember, sum/amount = 94/2 = 47.
so, he would have to score 47 points in each of the next 2 games to raise his general average score to 35.
