Question

ty received test Graves of 71%, 82%, 71%, 78% and 78%.A) what grade would he need to make on the 6th test to get a C if a C is at least 75% but less than 80%?B) is it possible for tie to get a b or better for his test average at least 80%?

Answer 1

As given that first 5grades are: 71%, 82%, 71%, 78% and 78%.

Let the 6th grade be C

a). Then:

`75\leq(71+82+71+78+78+C)/(6)\leq80`

Simplifying it:

`\begin{gathered} 75\leq(71+82+71+78+78+C)/(6) \\ 75*6\leq380+C \\ 450\leq380+C \\ 450-380\leq C \\ 70\leq C \end{gathered}`

And:

`\begin{gathered} (380+C)/(6)\leq80 \\ 380+C\leq480 \\ C\leq100 \end{gathered}`

So C should be in between 70 to 100.

b). For at least 80%:

`\begin{gathered} (71+82+71+78+78+C)/(6)\ge80 \\ 380+C\ge80*6 \\ 380+C\ge480 \\ C\ge100 \end{gathered}`

It is not possible for getting b grade as one cannot achieve more than maximum marks if the maximum marks are 100.