Sergio took four exams. He received good scores on three exams, but failed one. The teacher allows her student's to drop their lowest score. When Sergio does this, his average increases from 70 to 80. What was Sergio's failing exam score?
What was Sergio's failing exam score?
For 4 perfect exam scores Sergio would have had 400 total points, as it was he ended up with 70% of those points or
0.7*400 = 280 points
By dropping a test grade Sergio reduced the number of possible points to 300 and his grade improved to 80%
0.8*300 = 240 points
The difference between the two is the score (in points) Sergio received that lowered his original average
280 - 240 = 40 points
Assuming the test was out of a possible 100 points that means he got a 40% on that test.
Another way to look at this problem:
Let's look at the second situation first. The 3 test scores Sergio kept resulted in an average of 80 points. That means that those 3 test scores must add up to 240 (3X80).
Now, let's look at the first situation. The 4 test scores gave him an average of 70, so the 4 test scores must have added up to 280 (4X70).
Since we already know that the sum of the three test scores he kept is 240, we can find that the 4th test score equals 40 points by subtracting (280-240).
Mental math approach: Since the average score for the three exams increased by 10, the total increase is 30 points. The 30 points must be balanced with losing score. Therefore, the falling exam score is 70-30 = 40 points.