thomas needs to earn a b in his psychics class his current test scores are 88,90,77 and 77 his final exam is worth 4 test scores. in order to earn a B Thomas's average must lie between 80 and 89 inclusive. what range of scores can Thomas receive on the final exam to receive a B in the course?

Each exam that Thomas has already taken is assumed to be out of the norm of 100points. First add the test scores and divide it by the total points possible thus far (400):
88+90+77+77= 332
332/400=>83% B
Thomas already has a B in the course, so we know that the least he would have to do is maintain his current score of 332 on the final, which is worth 4 tests (400pts possible.) Now we will use trial and error by adjusting the score of 332 to get our results.
316/400 => 79% C (uh oh! too low!)
320/400 => 80% B
Bingo! Now we know Thomas needs as least 320 points on his final exam to get a B in the course! Lets test out our findings!
Total number of points possible with the final exam: 800
Total number of points earned (332) plus needed points (320): 652
652points / 800points possible => 81.5% B
We can see here that Thomas has a little bit of wiggle room on the final exam. He can still get a B in the course with a high C on the final! Observe:
332pts earned + 308pts on the final exam => 640pts earned / 800pts possible=> 80% B
Same way vice versa:
332pts earned + 388pts on the final exam => 720pts earned / 800pts possible => 90% A
The range of scores on the final exam Thomas would need to maintain a B in the course is from 308-387points. If he gets less than a 308 on the final he will get a C in the course. If he gets more than 387 on the final, he will obtain an A in the course.