Respuesta :
The Solution:
Given Polly's grades as:
[tex]70,85,90,88[/tex]Let the minimum grade she needs to average more than 85 be represented with x.
By formula,
[tex]\text{ Average grade =}\frac{\text{ sum of grades}}{\text{ number of grades}}[/tex]In this case,
[tex]\begin{gathered} \text{average grade =85} \\ \text{ sum of grades = 70+85+90+88+x} \\ \text{ number of grades = 5} \end{gathered}[/tex]Substituting, we get the inequality that describes the situation as below:
[tex]\text{ 85 }\leq\frac{70+85+90+88+x}{5}[/tex]The above inequality is the same as
[tex]\frac{70+85+90+88+x}{5}\ge85[/tex]Solving the above inequality, we multiply both sides by 5.
[tex]\begin{gathered} \frac{70+85+90+88+x}{5}\times5\ge(85\times5) \\ \\ 70+85+90+88+x\ge425 \end{gathered}[/tex][tex]333+x\ge425[/tex]Collecting the like terms, we get
[tex]\begin{gathered} x\ge425-333 \\ \\ x\ge92 \end{gathered}[/tex]Thus, the minimum grade Polly needs is 92.
Therefore, the correct answer is 92.
