How to Score 80 Points

Question

A basketball team is averaging 36 two point shots per game and making 14 of them for an average of 40%. They average 17 three point shots per game and make 6 for an average of 34%. Plus they are shooting 11 free throws per game and making 7 for 60%. They average 54 points per game. I want to know, if the shooting percentage and free throws remain unchanged, how many additional 2 and 3 point shots do they need to take to score 80 points per game?

Answer 1

Well, the percents are rounded a bit. 14/36 = 38.8%, 6/17 = 34.29-% and 7/11 = 63.63%

So indeed they average 14*2 + 6*3 + 7 *1 = 28 + 18 + 7 = 46+7 = 53 points per game.

That means, the average points per game must increase by 27 in order to meet the goal.

Since there is no interest in improving the free throw average, let x be the number of 2-point

field goals and y be the number of 3-point shots that must be attempted so that the goal is met.

Respecting the percents shown in the opening statement,rather than the rounded ones given in the

statement in the problem.

2*38.8% X + 3*34.29% Y = 27

0.7 X + 1.0287Y = 27 is the decimal equivalent equation

note that 7/9 = 0.7 so the equation can be written as (7/9) x + 1.0287 Y = 27

Multiplying both sides by 9/7 so as to clear the first fraction:

(9/7) ( (7/9) x + 1.0287 y ) = 27 * (9/7)

x + 1.3226142857y = 243/7

x = 243/7 - 1.3226142857y <--- please label this equation ALPHA

34 < 243/7 < 35

So if the team does not attempt any 3-point shots at all (y=0), they will need to attempt

AT LEAST 35 2-point field goal shots.

Since there is no second equation due to lack of data or contraints, the team's analyst can use the equation ALPHA in bold above to determine how many 2 point field shots need to attempted based on the

number of 3-point shot attempts that are available, which is most convenient for them.

For example, if they decided to play shallow and attempt an additional y=10 of 3-point shot attempts per game, then they will need to increase their 2 point shots attempts by x=22 per equation ALPHA. Specifically, when y=10, x=22 per equation ALPHA. That would bring their statistics to: 36+22 = 58 of the 2 point field goal attempts and 17 + 10 = 27 of the 3 point shot attempts

Of these, they will make 58 * 38.8% = 22 points

27 * 34.29% = 9 points

which is an ADDITIONAL 31 points.

That brings their average score to 53 + 31 = 84