SOLUTION: For a certain student, the average of ten test scores is 80. If the high and low scores are dropped, the average is 81. What is the average of the high and low scores?

Let x = the sum of highest and lowest scores

Let y = the sum of the middle 8 scores left 
        after the highest and lowest are dropped

Then x+y = the sum of all 10 scores

That says:

 

Multiply both sides by 10

 x + y = 800

That says the average of the middle 8 scores is 81, so

 

Multiply both sides by 10

     y = 648

Substitute in

   x + y = 800
 x + 648 = 800
       x = 152 = the sum of highest and lowest scores

Average of highest and lowest scores =  = 76

Edwin