Mrs. Marcincavage allowed each student in her math class to drop the lowest of their five test scores. When Matthew dropped the lowest of his test scores, a 60, his test average increased by 5 points. What is Matthew’s new test average?
If there were 5 tests, with average a, then compare total points earned:
5a - 60 = 4(a+5)
5a-60 = 4a+20
a = 80
To find Matthew's new test average, we need to determine his average before dropping the lowest score and calculate his average after dropping the lowest score.
Let's say Matthew's average before dropping the lowest score was X.
To find the initial average (before dropping the lowest score), we add up all his scores and then divide by the total number of scores (in this case, 5):
Initial Average:
(X + 60 + score2 + score3 + score4) / 5
After dropping the lowest score, his average increased by 5 points. Therefore, his new average is:
X + 5
We can now set up an equation to solve for X, which represents his initial average.
Equation 1: Initial Average = New Average - 5
(X + 60 + score2 + score3 + score4) / 5 = X + 5
To solve this equation, we can multiply both sides by 5 to eliminate the denominator:
X + 60 + score2 + score3 + score4 = 5X + 25
Next, we can combine like terms by subtracting X from both sides and rearranging the equation:
60 + score2 + score3 + score4 - 25 = 5X - X
35 + score2 + score3 + score4 = 4X
Now, we can isolate X by dividing both sides by 4:
(35 + score2 + score3 + score4) / 4 = X
So, X represents his initial average. To find Matthew's new average, we substitute X back into the equation X + 5.
New Average = X + 5 = [(35 + score2 + score3 + score4) / 4] + 5
This equation will give us Matthew's new test average. However, it is impossible to calculate the exact answer without knowing the values of score2, score3, and score4.