Question

erika needs a test average of 85 or higher to make the honor roll there are four tests in the term her first three test grades 78,80,and 88. which inequality could be used to find what she needs to score on her fourth test, x, in order to make the honor roll

Answer 1

First, notice that we want the average to be 85 or higher. We can write this like this:

$\mu\ge85$

where mu is the average.

We know that there are four tests, and there are already three grades: 78,80 and 88. Then if we calculate the mean we have:

$\begin{gathered} \mu=\frac{78+80+88+x}{4}=\frac{x+246}{4} \\ \Rightarrow\mu=\frac{x+246}{4} \end{gathered}$

but we already know that the average must be greater or equal than 85, then, combining both expressions we get the following:

$\begin{gathered} 85\le\mu=\frac{x+246}{4} \\ \Rightarrow\frac{x+246}{4}\ge85 \end{gathered}$

solving the inequality for x, we get:

$\begin{gathered} \frac{x+246}{4}\ge85 \\ \Rightarrow x+246\ge85\cdot4=340 \\ \Rightarrow x\ge340-246=94 \\ x\ge94 \end{gathered}$

therefore, Erika needs a score of 94 or higher in order to make the honor roll