Musical Instrument Participation Among High School Seniors and Non-Seniors

Understanding the dynamics of musical instrument participation among high school students can provide insights into the cultural and academic environments of schools. A specific high school with 500 students presents an interesting case study in this regard. This article illustrates how to solve complex statistical problems involving musical instrument participation, utilizing basic algebraic techniques.

Introduction

At a school comprising 500 students, the distribution of seniors and non-seniors who play musical instruments demonstrates a nuanced understanding of extracurricular activities. The problem at hand involves a detailed analysis to ascertain the precise number of non-seniors who play a musical instrument, given certain statistical parameters. This article will guide through the problem-solving process with step-by-step instructions and logical reasoning.

Problem Statement

A school with 500 students has the following details regarding musical instrument participation:

40 seniors play a musical instrument. 30 non-seniors do not play a musical instrument. 46.8% of the students do not play a musical instrument.

Step-by-Step Solution

To solve this problem, we will break it down into several steps, utilizing mathematical equations and algebraic manipulation to find the desired solution.

Determining the Number of Seniors and Non-Seniors

Let:

S Number of Seniors

N Number of Non-Seniors

Total number of students S N 500

Given the total number of students:

Total number of students: 500

Calculating the Number of Students Who Do Not Play a Musical Instrument

Given that 46.8% of the students do not play a musical instrument:

0.468 x 500 234 students do not play a musical instrument.

Determining the Number of Seniors Who Do Not Play a Musical Instrument

40 seniors play a musical instrument, which implies:

Seniors who do not play 0.60S

Determining the Number of Non-Seniors Who Do Not Play a Musical Instrument

30 non-seniors do not play a musical instrument. Therefore, the number of non-seniors who play a musical instrument is:

Non-seniors who do not play 0.30N

Setting Up the Equation for Students Who Do Not Play a Musical Instrument

Combining the numbers from the previous steps, we can set up the equation:

0.60S 0.30N 234

From the total number of students (500 S N), we can express N in terms of S:

N 500 - S

Substitute N in the equation:

0.60S 0.30(500 - S) 234

Simplify the equation:

0.60S 150 - 0.30S 234

0.30S 150 234

0.30S 234 - 150

0.30S 84

S 84 / 0.30 280

Calculating the Number of Non-Seniors

Substitute S 280 back into the equation (500 S N):

N 500 - 280 220

Therefore, the number of non-seniors is 220.

Calculating the Number of Non-Seniors Who Play a Musical Instrument

Given that 30 non-seniors do not play a musical instrument, the number of non-seniors who play a musical instrument is:

Non-seniors who play 220 - 30 154

Thus, the number of non-seniors who play a musical instrument is 154.