There are 40 students in a class. The teacher gave each female student 5 counters and each male student 3 counters. After the distribution of the counters, the teacher realized that the female students had 128 more counters than the male students. Write and solve a linear equation to find the number of female students in the class.

2. Since there are only female and male students in the problem, the number of male students can be shown as 40 - x, the total number of students subtracted from the number of female students.

3. To find the number of counters each group has, you can multiply their variable by the number of counters each student recieves. The female students have 5x counters, and the male students have 3(40-x) counters.

4. Since the female students have 128 more than the male students, you can say that the male students' counters are equal to the female students' counters minus 128.

5. Then, you put all of that into an equation. The female number of counters minus 128 is equal to the male number of counters and solve.

Simplified way:

Female students: x

Male students: 40-x

Female # of counters: 5x

Male # of counters: 3 (40-x)

5x - 128 = 3 (40-x)

5x - 128 = 120 - 3x

8x -128 = 120

8x = 248

x = 31

You can also check by plugging it in:

5(31) - 128 = 3 (40-31)

155 - 128 = 3 * 9

27 = 27

:)