To earn a B in your Algebra class, you must achieve an unrounded test average between 84 and 86 (inconclusive). You scored 86,85, and 80 on the first three tests of the grading period. What possible scores can you earn on the fourth and final test to earn a B in the course?

so far you have a total of 251

lowest mark needed:
(251+x)/4 >84
251+x > 336
x > 85

highest mark needed:
(251+x)/4 < 86
251+x < 344
x < 93

possible scores are 86, 87, 88, 89, 90, 91, and 92

Question: why would you NOT want a score highter than 86 ?

To determine the possible scores on the fourth test that would result in earning a B in the course, we need to consider the target range for the unrounded test average.

Let's denote the score on the fourth test as "x".

To calculate the unrounded test average, we need the sum of all four test scores:

Sum of scores = 86 + 85 + 80 + x

We want the unrounded average to be between 84 and 86, so we can set up the following inequality:

84 ≤ (Sum of scores) / 4 ≤ 86

Multiplying both sides of the inequality by 4, we have:

336 ≤ (Sum of scores) ≤ 344

Substituting the expression for the sum of scores, we get:

336 ≤ (86 + 85 + 80 + x) ≤ 344

Simplifying, we have:

336 ≤ 251 + x ≤ 344

Subtracting 251 from all parts of the inequality, we get:

336 - 251 ≤ x ≤ 344 - 251

85 ≤ x ≤ 93

Therefore, to earn a B in the course, you can score any value between 85 and 93 on the fourth test.

To determine the possible scores you can earn on the fourth and final test to earn a B in the course, we need to find the range of values that will result in an unrounded test average between 84 and 86.

Let's calculate the minimum and maximum possible averages.

Minimum average:
To find the minimum average, we consider the lowest possible score you can earn on the fourth test. Assuming all other test scores remain the same, the lowest possible score is 0. Thus, the minimum average would be (86 + 85 + 80 + 0) / 4 = 251 / 4 = 62.75.

Maximum average:
To find the maximum average, we consider the highest possible score you can earn on the fourth test. Assuming all other test scores remain the same, the highest possible score is 100. Thus, the maximum average would be (86 + 85 + 80 + 100) / 4 = 351 / 4 = 87.75.

Since we need an unrounded test average between 84 and 86, the possible scores you can earn on the fourth and final test to earn a B in the course are any scores that result in an average between 62.75 and 87.75 (inclusive).