Final answer:
Peter must score at least an 85 on his fifth math exam to achieve an overall average of 80 and secure at least a B in his math class. The number line of possible scores for his fifth exam that ensure a B would start at 85 and go up to the maximum score of 100.
Step-by-step explanation:
To determine the score that Peter needs on his fifth exam to get at least a B in his math class, we first need to establish the average score he requires. Peter's current scores are 70, 85, 76, and 84. If we assume that a B requires an average score of at least 80 across five exams, we can set up an equation to find the minimum score Peter needs on his fifth exam.
Let x be the score Peter needs on the fifth exam. The average score is found by adding all the scores together and dividing by the number of scores, which in this case is five. So, we need to solve the following equation for x:
(70 + 85 + 76 + 84 + x) / 5 ≥ 80
Adding the known exam scores gives us 315 + x. Multiplying both sides of the inequality by 5 to get rid of the denominator, we have:
315 + x ≥ 400
Subtracting 315 from both sides, we find:
x ≥ 85
Therefore, Peter needs to score at least an 85 on his fifth exam to achieve an average score of 80 and get a B in the class. The number line representing scores that Peter can get on the fifth exam to earn at least a B would start at 85 and extend to 100, since 100 is the maximum possible score on an exam.