Algebra Word Problem: Student Population Change

Published on August 6, 2026

Word-Problem

Solve a system of equations based on a changing student population. Calculate last year's male and female student numbers and this year's male student numbers.

Question

Answer

To solve this problem, we will translate the Japanese text into mathematical equations.

1. Analyze the Problem Statement

Text Translation:
"There is a junior high school where the total number of students (male and female combined) last year was 450. This year, the number of boys decreased by

and the number of girls increased by

, resulting in a total increase of 18 students in the entire school population.

(1) Let the number of boys last year be

and the number of girls last year be

. Find

and

. (Answer in the format

without units. Example:

)

(2) Find the number of boys this year. (Answer without units. Example:

2. Step-by-Step Solution

Part (1): Find the number of boys () and girls () last year.

From the problem, we can derive two equations:

Equation 1: Total students last year
The sum of boys and girls last year was 450.

Equation 2: Change in student population
The number of boys decreased by

(

) and the number of girls increased by

(

), leading to a net increase of 18 students.

To make Equation 2 easier to work with, let’s multiply the entire equation by 100 to remove the decimals:

Now we have a system of linear equations:

From Equation 1, we can express

in terms of

Substitute this into Equation 2:

Now, find

Wait, let me re-check the provided answer in the image. The image says "答え

". Let’s check if those values satisfy the conditions.
If

Total: (Correct)
Change: ; .
Net change: .
The problem states the increase was 18, not 9.

Let’s re-read the image carefully.
“男子が

減少し, 女子が

増加したので全校生徒が

人増加した。”

, then

.
There might be a typo in the image’s provided answer or the problem text. Let’s re-calculate based on the text provided.

If the increase was 18:

Subtracting the equations:

Let’s check the image again. Is it possible the increase was 9? Or is it possible the decrease was

?
If

and the increase is 18:

.
If the decrease was

.
If the increase was

Actually, looking at the image’s answer

, let’s see what change would result in 18.

(11%).
Or

(4%).

Conclusion on Part 1: Based strictly on the text provided in the image (increase of 18, decrease of 10%, increase of 8%), the mathematical solution is

. However, the image provides an answer key of

. This suggests a typo in the problem’s numbers in the original source. I will provide the solution based on the text’s numbers.