Tom took five math tests and got an integer score on each of them. He never scored higher than 90, and his lowest score was the fourth test. If his average score, rounded to the nearest integer, was 82, what is the lowest possible score he could have gotten on the fourth test?
50
To find the lowest possible score on the fourth test, we need to consider the given information.
We know that Tom took five math tests and got an integer score on each of them. His lowest score was the fourth test. This means that the fourth test score is lower than the other four scores.
We also know that Tom never scored higher than 90. This indicates that the highest score on the other four tests is less than or equal to 90.
Lastly, we are given that Tom's average score, rounded to the nearest integer, is 82. This means that the sum of all five test scores divided by 5 is approximately equal to 82.
Let's assume the lowest score on Tom's fourth test is 'x'. To find the lowest possible value for 'x', we can set up an equation.
(x + (score on test 1) + (score on test 2) + (score on test 3) + (score on test 5)) / 5 ≈ 82
Simplifying the equation, we get:
(x + (sum of the other four test scores)) / 5 ≈ 82
To ensure that 'x' is the lowest possible score, we want to maximize the sum of the other four test scores. Since the highest score on the other four tests cannot exceed 90, the sum of the other four test scores will be 90 + 90 + 90 + 90 = 360.
Substituting the values into the equation:
(x + 360) / 5 ≈ 82
Multiplying both sides of the equation by 5:
x + 360 ≈ 410
Subtracting 360 from both sides of the equation:
x ≈ 50
Therefore, the lowest possible score Tom could have gotten on the fourth test is 50.