The class average is 83, take away the best score then the average is 82. There are 16 students, what is the best score?

Question

The class average is 83, take away the best score then the average is 82. There are 16 students, what is the best score?

Answer 1

Here's a simple way of looking at the problem:

16*83=1328 (83 average with 16 students)

15*82=1230 (82 average with 15 students)

1328-1230=98, as was shown

The answer was given twice but it's just another strategy for solving a problem like this.

Answer 2

Let x = the best score

 

And if you take away the best score and the class average is 82, this would imply the sum of the scores being the product of 82 and 15 because adding the best score makes for the 16th student.

 

Hence the equation to solve for x is simply the sum of the product of 82 and 15 and x divided by 16 equals 83.

 

(82*15+x)/16=83 Multiply bothe sides of the equation by 16 to simplify the arithematic.

 

  1230+x=83*16=1328

 -1230                -1230

 

x=98  Therefore, the highest score was a 98.

Answer 3

let x be the total points for all students

let y be the best score

 

 

x/16 = 83         -------> x = 83*16 = 1328

 

(x - y)/ 15 = 82

 

(1328 - y)/15 = 82

 

1328 - y = 15 * 82

 

1328- y = 1230

 

1328 - 1230 = y

 

y = 98