Question

There are 25 students in Mrs. Wang's first period algebra class. On Monday, five students were absent and the other 20 students took a test. The average grade for those students was $86 .$ The next day after the five absent students took the test, the class average was $88 .$ What was the average of those five students' grades? $$\begin{array}{ll}{\text { (A) }} & {90} \\ {\text { (B) }} & {92} \\ {\text { (C) }} & {94} \\ {\text { (D) } 96}\end{array}$$

Name: Problem 5, Chapter :
Uploaded: 2019-05-02T16:55:29-08:00
Duration: 1 min 33 s
Channel: Lily An
Description: There are 25 students in Mrs. Wang's first period algebra class. On Monday, five students were absent and the other 20 students took a test. The average grade for those students was 86 . The next day after the five absent students took the test, the class average was 88 . What was the average of those five students' grades? (A) 90 (B) 92 (C) 94 (D) 96

   There are 25 students in Mrs. Wang's first period
algebra class. On Monday, five students were absent
and the other 20 students took a test. The average
grade for those students was $86 .$ The next day after
the five absent students took the test, the class average
was $88 .$ What was the average of those five students'
grades?
$$\begin{array}{ll}{\text { (A) }} & {90} \\ {\text { (B) }} & {92} \\ {\text { (C) }} & {94} \\ {\text { (D) } 96}\end{array}$$

Instant Answer

Solved by Expert Lily An

05/02/2019

Step 1

So, the total grade of these 20 students is $20 \times 86$. Show more…

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There are 25 students in Mrs. Wang's first period algebra class. On Monday, five students were absent and the other 20 students took a test. The average grade for those students was $86 .$ The next day after the five absent students took the test, the class average was $88 .$ What was the average of those five students' grades? $$\begin{array}{ll}{\text { (A) }} & {90} \\ {\text { (B) }} & {92} \\ {\text { (C) }} & {94} \\ {\text { (D) } 96}\end{array}$$

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Key Concepts

Arithmetic Mean

The arithmetic mean is the sum of a set of values divided by the number of values. It is a statistical measure used to find the central tendency of data, which in many scenarios like test scores reflects the overall performance of a group.

Weighted Average

A weighted average is used when different groups or subsets contribute to an overall average at different proportions. In contexts where subsets have distinct averages and sizes, the total sum of values across groups is divided by the combined total number of items to obtain the overall average.

Algebraic Equation Setup

Setting up and solving algebraic equations involves expressing unknown quantities in terms of known values. By representing the total sum of scores using the average multiplied by the number of scores, equations can be created to isolate and solve for unknown group averages, making this a crucial technique in problems involving aggregated data.

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