Question

Brad scored 87, 71, 72, 74, and 86 on his five tests during the semester. The average of those scores counts for two-thirds of his final grade. He has a final exam at the end of the semester that will count for the other one-third. To get a B, his final grade must be greater than or equal to 80 and less than 90. Solve for the range of grades x that he could score on his final exam that would result in him getting a B. Give your answer as an inequality. Assume that 100 is the greatest possible grade.

a) 80 ≤ x < 90
b) 70 < x ≤ 80
c) x ≥ 90
d) x < 70

Answer 1

Brad could score on his final exam in order to get a B is x ≥ 84.

Step-by-step explanation:

To find the range of grades that Brad could score on his final exam in order to get a B, we need to consider the weight of his average test scores and the desired final grade range. The average of Brad's five test scores counts for two-thirds of his final grade, while the final exam counts for one-third. Let's calculate his average:

Average = (87 + 71 + 72 + 74 + 86) / 5 = 78

Now, let x represent the grade Brad can score on his final exam. We want his final grade to be greater than or equal to 80 and less than 90 in order to get a B. Therefore, we can set up the inequality:

78 * (2/3) + x * (1/3) ≥ 80

Simplifying the inequality:

(2/3)(78) + (1/3)(x) ≥ 80

52 + x/3 ≥ 80

x/3 ≥ 80 - 52

x/3 ≥ 28

x ≥ 84

Therefore, the range of grades x that Brad could score on his final exam to achieve a B is x ≥ 84. This can be written as the inequality x ≥ 84.