• 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} (76+81+51+75+x)/(5)=70 \\ (283+x)/(5)=70(*5) \\ 283+x=350 \\ x=350-283 \\ x=67 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/1gkvwn4xst4qi8bq9nuumdw9kvvfrud3xs.png)
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} (76+81+51+75+y)/(5)=80 \\ (283+y)/(5)=80(*5) \\ 283+y=400 \\ y=400-283 \\ y=117 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/tikmvgggk83bj16exungbeq3uf2xwc1nox.png)
Thus, in this scenario, he has to score 117 points to get a B