Question

On the first four exam your grades are 76,78,73 and 77. You are hoping to earn a C in the course. This will occur if the average of your fifth exam grades is greater than or equal to 70 and less than 80. What range of grades on the fifth exam will result in earning a C?

Answer 1

Answer:

greater than or equal $46$ to and less than $96$

Step-by-step explanation:

GIVEN: On the first four exam your grades are $76,78,73$ and $77$. You are hoping to earn a C in the course. This will occur if the average of your fifth exam grades is greater than or equal to $70$ and less than $80$.

TO FIND: range of grades on the fifth exam will result in earning a C.

SOLUTION:

Total number of marks scored till first four exams $=76+78+73+77$

                                                                                  $=304$

let average marks scored after fifth exam be $S$.

let marks scored in fifth exam be $x$

$S=\frac{76+78+73+77+x}{5}$

$S=\frac{304+x}{5}$

Now, to earn a C the average must be greater than or equal to $70$ and less than $80$

                    $70\leq S< 80$

                    $70\leq \frac{304+x}{5}$

when

 $\frac{304+x}{5}\geq 70$

$304+x\geq 350$

$x\geq 46$

when

 $\frac{304+x}{5}$

 $304+x$

 $x$

Hence grades in fifth exam must be greater than or equal $46$ to and less than $96$