I need to know what his lowest score can be to still keep an average score of 90

Question

Joseph has scores of 87, 89, and 92 on his first three weekly algebra assessments.
What score must he get on the Week 4 Assessment to have an average of 90 or better for the four assessment

Answer 1

This is a very common type of question to think about averages a little less directly.

 

An average is a sum of some items divided by the total number of items. For example, if I scored 87, 89, 92, and 89 on my four tests, I would find my average test score by computing (87 + 89 + 92 + 89)/4 = 357/4 = 89.25.

 

Let's call our unknown score x. We know that the average (87 + 89 + 92 + x)/4 ≥ 90. Let's solve this inequality for x!

 

First, add up the like terms in the parentheses:

(87 + 89 + 92 + x)/4 ≥ 90

(268 + x)/4 ≥ 90

 

Now, multiply both sides by 4 to undo the fraction on the left hand side. Because 4 is a positive number, this won't change the direction of the inequality:

(268 + x) ≥ 90 * 4

268 + x ≥ 360

 

Finally, subtract 268 from both sides to solve for the minimum value of x:

x ≥ 360 - 268

x ≥ 92

 

You must score at least a 92 in order to have an average of 90 or better.