An arithmetic student needs at least a 70% average to receive credit for the course. If she scored 86%, 77%, and 64% on the first three exams, what is the lowest score she can get on the fourth exam to receive credit for the course?
There's a total of 100% for 4 exams. Her total number of points must be at least 0.7 * 400 = 280 to pass.
After three tests she has 227 points. 280 - 227 = 53.
If she gets 53% on the fourth exam, she'll pass with a 70%.
53
To determine the lowest score the student can get on the fourth exam to receive credit for the course, we need to consider the current average and what score is required to reach at least a 70% average.
First, let's find the student's current average by calculating the average of the first three exam scores:
(86 + 77 + 64) / 3 = 227 / 3 = 75.67%
Next, we need to determine how much the student needs to improve her average to reach at least 70%. We subtract 70% from her current average:
75.67% - 70% = 5.67%
To find the lowest score she can get on the fourth exam, we need to calculate what that score would average out to with her current scores. We need to add this average to her current average to reach the desired average:
70% + 5.67% = 75.67%
So, to maintain at least a 70% average overall, the student will need to score at least 75.67% on the fourth exam.
To find the lowest score the student can get on the fourth exam and still achieve a 70% average, we can use the concept of weighted averages.
The average score for the four exams should be at least 70%. This means that the student's total score for all four exams divided by 4 should be equal to or greater than 70.
Let's use the variable "x" to represent the score the student can get on the fourth exam.
To calculate the average, we need to add up the scores of the four exams and divide the sum by 4:
(86 + 77 + 64 + x) / 4 ≥ 70
To find the lowest score, let's solve for "x".
86 + 77 + 64 + x ≥ 70 * 4
227 + x ≥ 280
Now, let's isolate "x" by subtracting 227 from both sides of the inequality:
x ≥ 280 - 227
x ≥ 53
Therefore, the lowest score the student can get on the fourth exam and still achieve a 70% average is 53%.