5 players received a score from 0-100 inclusive. Their average score was 80. What maximum number of players could have scored 50?

Question

Please give a step-by-step solution to the SAT question.

Thanks.

Answer 1

If the average score was 80, the total of all the scores had to be 80*5 = 400.

 

If 2 players scored 50, that's 100 points total for them.  So the other 3 players would have to score a total of 300 to get to 400.  That's possible but it means that the other 3 players would all have to have scored 100.

 

If any more than 2 players scored 50, then the other players would have to average MORE than 100 to make up for the missing points out of the needed total of 400.  So 2 is the maximum.

 

 

Answer 2

2 had 50%, 3 had 100%

 

5 * 80 = 400 total points for everyone

 

50 being targeted score, and 100 being the maximum score.

a= number of 50

b= number of 100

 

50a + 100b = 400

50a + 50(2a) = 400

4a = 8

a = 2