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?
To find out the lowest score the student can get on the fourth exam to receive credit for the course, we need to calculate the average score after all four exams and see if it meets the minimum requirement of 70%.
We already know the scores of the first three exams: 86%, 77%, and 64%.
Step 1: Calculate the total score on the first three exams.
Total score = 86% + 77% + 64%
Step 2: Calculate the average score on the first three exams.
Average score = Total score / 3
Step 3: Determine the lowest score needed on the fourth exam.
To find the lowest possible score, we assume this score as 'x'.
Step 4: Calculate the total score after four exams.
Total score after four exams = Total score + x
Step 5: Calculate the average score after four exams.
Average score after four exams = Total score after four exams / 4
Step 6: Set up an equation to find the lowest score needed on the fourth exam.
Average score after four exams >= 70%
Using the above information, we can now solve for the lowest score 'x' that gives an average of at least 70%.
Average score after four exams = (Total score + x) / 4
Setting up the equation:
(86% + 77% + 64% + x) / 4 >= 70%
Simplifying the equation:
(227% + x) / 4 >= 70%
To find the lowest possible score the student can get, we rearrange the equation:
227% + x >= 4 * 70%
227% + x >= 280%
Subtracting 227% from both sides:
x >= 280% - 227%
Calculating the minimum score needed:
x >= 53%
Therefore, the student needs to score at least 53% on the fourth exam in order to receive credit for the course, given her previous exam scores.