Question

A student scored 83 and 91 on their first two quizzes. Write and solve a compound inequality to find the possible values for a third quiz score that would give them an average between 85 and 90, inclusive.

Answer 1

Answer:

3*85 <= 83+91+x <= 3*90 

255 <= 174+x <= 270 

81 <= x <= 96

Answer 2

81 ≤ x ≤ 96

The possible values for the third quiz are 81, 82, 83, 84, ... ..., 95, 96.

Given:

A student scored 83 and 91 on his first two quizzes.

To find:

Write and solve a compound inequality to find the possible values for a third quiz score that would give him an average between 85 and 90, inclusive.

Step-by-step explanation:

Let the third quiz score be x.

∴ total score of the three quizzes is (83 + 91 + x) = 174 + x.

∴ average score = $\dfrac{174+x}{3}$

Since the average score should be between 85 and 90, inclusive, required inequality be

85 ≤ $\dfrac{174+x}{3}$ ≤ 90

➜ 255 ≤ 174 + x ≤ 270

➜ 255 - 174 ≤ x ≤ 270 - 174

➜ 81 ≤ x ≤ 96

The possible values for the third quiz are 81, 82, 83, 84, ... ..., 95, 96.

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