Henry took five tests. His average score was 57 points. He scored at least 50 points on each test. There were 100 points possible on each test. What is the highest score that Henry could have earned on any of the five tests?
To find the highest score that Henry could have earned on any of the five tests, we need to determine the lowest possible scores he could have gotten on the other tests. Since his average score was 57 points and he scored at least 50 points on each test, the sum of his scores on the five tests would be at least 5 × 50 = 250.
If the sum of the scores on the five tests is 250 and there were 100 points possible on each test, then the highest score Henry could have earned on any of the tests is the remaining points after subtracting the sum of the scores on the other four tests from 500 (100 points per test × 5 tests).
Let's calculate:
Total points possible on 5 tests = 100 points per test × 5 tests = 500 points
Minimum possible total score on 5 tests = Average score × Number of tests = 57 points × 5 tests = 285 points
Remaining points for the highest score = Total points possible - Minimum possible total score = 500 - 285 = 215 points
Therefore, the highest score that Henry could have earned on any of the five tests is 215 points.
To find the highest score Henry could have earned on any of the five tests, we need to consider that his average score was 57 points and he scored at least 50 points on each test. Since there are five tests in total, if Henry's average score was 57, then he earned a total of 57 * 5 = 285 points in total.
Since Henry scored at least 50 points on each test, we can subtract the minimum possible scores (50 * 5 = 250 points) from his total score. This leaves us with 285 - 250 = 35 points that are the maximum scores he earned above the minimum on any of his five tests.
Therefore, the highest score Henry could have earned on any of the five tests is 35 points.
total points: 285
4*50 + 85 = 285
making more than 50 on any of the other 4 tests would reduce the highest score.