First, notice that we want the average to be 85 or higher. We can write this like this:
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:
but we already know that the average must be greater or equal than 85, then, combining both expressions we get the following:
solving the inequality for x, we get:
therefore, Erika needs a score of 94 or higher in order to make the honor roll