You can put this solution on YOUR website! One team scored 4 runs less than the other team. The average of the squares of their scores was 53. What are their scores?
:
Let x = score of one team
then
(x+4) = score of another team
:
WRite an equation for this statement:
"The average of the squares of their scores was 53. = 53
Multiply equation by 2 to get rid of the denominator
x^2 + (x+4)^2 = 2(53)
:
x^2 + x^2 + 8x + 16 = 106; FOILed (x+4)(x+4)
:
2x^2 + 8x + 16 - 106 = 0
:
2x^2 + 8x - 90 = 0; our old friend, the quadratic equation appears!!!
:
This factors to:
(2x - 10)(x + 9) = 0
:
Positive solution
2x = 10
x = 10/2
x = 5 one team's score
:
Another team's score: 5 + 4 = 9
:
Check solutions in the statement
""The average of the squares of their scores was 53." = = = 53
