Question

Assume that in one of the classes the student has earned test scores of 76, 81, 51, 75, and only one test remains. if the student needs a mean score of 70 to earn a C, then what must the student obtain on the final test? _______if the student needs a mean score of 80 to earn a B, then what must the student obtain on the final test? ________

Answer 1

• 67

,

• 117

1) Since there are 5 tests, only one left and we want to know the mean, and this has to be greater than or equal to 70 so that he earns a C, we can write out:

$\begin{gathered} \frac{76+81+51+75+x}{5}=70 \\ \frac{283+x}{5}=70(\times5) \\ 283+x=350 \\ x=350-283 \\ x=67 \end{gathered}$

Note that we had to multiply both sides by 5 to get rid of the fraction.

2) Hence, the grade this student has to take it's 67

For the same scenario but the student needs to earn a B, then we can write out the following with a slight difference:

$\begin{gathered} \frac{76+81+51+75+y}{5}=80 \\ \frac{283+y}{5}=80(\times5) \\ 283+y=400 \\ y=400-283 \\ y=117 \end{gathered}$

Thus, in this scenario, he has to score 117 points to get a B