A student earned scores of 85, 90, 88, and 92 on the first four quizzes of the semester. W… — ACT

A student earned scores of $85$ , $90$ , $88$ , and $92$ on the first four quizzes of the semester. What score must the student earn on the fifth quiz to have an average (arithmetic mean) score of exactly $90$ for all five quizzes?

A
1
B
5
C
89
D
90
95Answer

Answer

The student must earn a score of 95 on the fifth quiz.

To find the score needed on the fifth quiz to achieve an average of

90

, first find the total number of points required. An average of

90

5

quizzes requires a total sum of

5 \times 90 = 450

points. The sum of the first four quiz scores is

85 + 90 + 88 + 92 = 355

points. Subtracting the current sum from the required total sum (

450 - 355

) yields

95

, which is the score the student must earn on the fifth quiz.

Step-by-Step Solution

Calculate the sum of the student's scores on the first four quizzes.

85 + 90 + 88 + 92 = 355

To find the total number of points the student has earned so far.

Calculate the total sum of points required to achieve an average of

90

over five quizzes.

5 \times 90 = 450

The arithmetic mean formula is Mean = Sum / Count, which can be rearranged to Sum = Mean * Count.

Subtract the sum of the first four quiz scores from the required total sum of five quiz scores.

450 - 355 = 95

The difference represents the score needed on the fifth quiz to achieve the target average.

Key Concept

Finding a missing value given a target arithmetic mean

Question

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Step-by-Step Solution

Key Concept

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