You can use variable in place of the fourth test score and inequality to get the needed minimum score.
The minimum score the student needs to get on the fourth test for the given condition is 90
Mean of a collection of values is the ratio of those values' sum to the count of those values(count means how many values are there).
Mean and average are same thing.
Let the fourth test score be 't'
Then we have 4 scores as 83, 90, 85, t
Their mean is found as
[tex]\overline{x} = \dfrac{\sum x}{n} = \dfrac{83 + 90 + 85 +t}{4} = \dfrac{258+ t}{n}\\[/tex]
Since average needs to be at least 87, thus,
[tex]\overline{x} \geq 87\\\\\dfrac{258 + t}{4} \geq 87\\\\\text{Multiplying 4 on both the sides}\\\\258 + t \geq 348\\\\\text{Subtracting 258 from both the sides}\\t \geq 90[/tex]
Thus, t needs to be at least 85 for the average to be 87 or above.
Since the problem is to find the minimum test score needed for the fourth test and since the minimum value of t is 90, thus,
The minimum score the student needs to get on the fourth test for the given condition is 90
Learn more about inequalities here:
https://brainly.com/question/13675572
