Questions: A mean of 60 on all exams is needed to pass a course. On his first five exams Lamond Paine's grades are 51, 59, 65, 81, and 54. (a) What is the minimum grade that Lamond can receive on the sixth exam to pass the course? (b) An average of 70 is needed to get a C in the course. Is it possible for Lamond to get a C? (a) The minimum grade that Lamond can receive on the sixth exam to pass the course is .

A mean of 60 on all exams is needed to pass a course. On his first five exams Lamond Paine's grades are 51, 59, 65, 81, and 54. (a) What is the minimum grade that Lamond can receive on the sixth exam to pass the course? (b) An average of 70 is needed to get a C in the course. Is it possible for Lamond to get a C? (a) The minimum grade that Lamond can receive on the sixth exam to pass the course is .
Transcript text: A mean of 60 on all exams is needed to pass a course. On his first five exams Lamond Paine's grades are 51,59, 65,81 , and 54 . (a) What is the minimum grade that Lamond can receive on the sixth exam to pass the course? (b) An average of 70 is needed to get a C in the course. Is it possible for Lamond to get a C? (a) The minimum grade that Lamond can receive on the sixth exam to pass the course is $\square$ .
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Solution

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Solution Steps

Step 1: Calculate the Total Score Needed to Pass

To pass the course, Lamond needs an average of 60 on all six exams. Therefore, the total score needed is:

\[ \text{Total score needed} = 60 \times 6 = 360 \]

Step 2: Calculate the Current Total Score

Lamond's current total score from the first five exams is:

\[ 51 + 59 + 65 + 81 + 54 = 310 \]

Step 3: Determine the Minimum Grade Needed on the Sixth Exam

To find the minimum grade Lamond needs on the sixth exam to pass, we set up the equation:

\[ 310 + x = 360 \]

Solving for \(x\), we get:

\[ x = 360 - 310 = 50 \]

Final Answer

(a) The minimum grade that Lamond can receive on the sixth exam to pass the course is \(\boxed{50}\).

(b) To get a C, Lamond needs an average of 70, which means a total score of:

\[ 70 \times 6 = 420 \]

Since his current total is 310, the score needed on the sixth exam is:

\[ 420 - 310 = 110 \]

Since 110 is not a possible score on a single exam, it is not possible for Lamond to get a C.

(b) It is not possible for Lamond to get a C.

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