Question

To pass a course with a C grade a student must have an average of 70 greater. A students grades on three test are 67, 72 and 63. Find what score the student must get on the next test to get a C average or better.

Answer 1

In order to calculate the value of the last calification that the student needs to acquire a C or higher, you write the following algebraic equation, which is used to calculate average values of a set of values:

$\frac{67+72+63+x}{4}\ge70$

The previous equation means that the average of the califications must be, at least, of 70 points. x is the last calification which you are looking for.

Then, you solve the previous inequality for x:

$\begin{gathered} \frac{67+72+63+x}{4}\ge70 \\ \frac{202+x}{4}\ge70 \\ 202+x\ge4(70) \\ x\ge4(70)-202 \\ x\ge280-202 \\ x\ge78 \end{gathered}$

Hence, the student has to obtain at leats 78 poins to pass the course.