Thomas needs a b in his class. his current test scores are 88, 83, 86 and 72. his final exam is worth 3 test scores. In order to ear a b Thomas average must lie between 80 and 89 inclusive. what range of scores can Thomas receive on the final to earn a b in the class?

80 ≤ [(88 + 83 + 86 + 72 + 3x) / 7] ≤ 89

80≤329+3x/7≤89

Multiply everything by "7"
560≤329+3x≤623
Subtract everything by "329"
231≤3x≤294
Divide everything by "3"
77≤x≤42

Thomas has to receive at least a 77.

To determine the range of scores Thomas can receive on the final exam to earn a B in the class, we need to find the minimum and maximum scores he can achieve while still maintaining an average between 80 and 89 inclusive.

First, let's calculate Thomas's current average test score by adding up his four test scores and dividing by 4:

(88 + 83 + 86 + 72) / 4 = 329 / 4 = 82.25

Now, we need to determine the minimum and maximum possible scores on the final exam that would result in an average between 80 and 89.

The maximum score on the final exam would be the highest possible score that, when averaged with his current test scores, still results in an average of 89. To find this, we multiply 89 by 7 (since the final exam is worth 3 test scores) and subtract his current test scores:

(89 * 7) - 329 = 623 - 329 = 294

So, the maximum score Thomas can get on the final exam is 294.

Next, we need to find the minimum score on the final exam that, when averaged with his current test scores, results in an average of 80. To find this, we multiply 80 by 7 and subtract his current test scores:

(80 * 7) - 329 = 560 - 329 = 231

Therefore, the minimum score Thomas can get on the final exam is 231.

In summary, Thomas can receive a score between 231 and 294 on the final exam in order to earn a B in the class.