The formula to calculate the average of a set of numbers is:
[tex]\text{ Average }=\frac{\text{ Total sum of all values}}{\text{ Total number of values}}[/tex]On the other hand, let it be x the score Reuben must get on the next test. Then, we have:
[tex]\begin{gathered} \text{ Average }=\frac{70+75+83+80+x}{5} \\ \text{ Average }=\frac{308+x}{5} \end{gathered}[/tex]Since the average has to be at least 80, that is, greater than or equal to 80, we can write the following inequality:
[tex]\begin{gathered} \text{ Average }\ge80 \\ $\boldsymbol{\frac{308+x}{5}\ge80}$ \end{gathered}[/tex]Now, we solve for x the inequality:
[tex]\begin{gathered} \frac{308+x}{5}\ge80 \\ \text{ Multiply by 5 from both sides} \\ \frac{308+x}{5}\cdot5\ge80\cdot5 \\ 308+x\ge400 \\ \text{ Subtract 308 from both sides} \\ 308+x-308\ge400-308 \\ $\boldsymbol{x\ge92}$ \end{gathered}[/tex]Therefore, Reuben must score 92 or higher on the next quiz to achieve an average of at least 80.
