Question

Just looking for the answers and how to solve them. This is a two-parter question and it’s a homework assignment. Would you be able to bold the answers

Answer 1

The average of the three grades is given by:

`average=(84+95+x)/(3)`

where x is the grade of the final exam.

(a) So, in order to have an average of at least 90, the grade x must be:

`\begin{gathered} (84+95+x)/(3)=90 \\ \\ 84+95+x=90\cdot3 \\ \\ 179+x=270 \\ \\ x=270-179 \\ \\ x=91 \end{gathered}`

Therefore, to earn an A in the course, you must get at least 91 on the final.

(b) If the final average is less than 80, we have:

`\begin{gathered} (84+95+x)/(3)<80 \\ \\ 84+95+x<80\cdot3 \\ \\ 179+x<240 \\ \\ x<240-179 \\ \\ x<61 \end{gathered}`

Therefore, the grades on the final that will cause this to happen are the grades that are less than 61.