Problem:

In a class of 35 students, the number of males is 15 more than the number of females. How many males and females are there in the class?

Solution:

Let m be the number of males in the class

Then let f be the number of females in the class.

In representation of the students in the class:

Equation 1:

• m + f = 35

Equation 2:

• 15 + f = m

Then, let's solve the linear equation using by substitution method.

Substitute the given value of m into the first equation. Then, solve the equation.

• m + f = 35
• (15 + f) + f = 35
• 15 + 2f = 35
• 2f = 35 - 15
• 2f = 20
• 2f/2 = 20/2
• f = 10

Substitute the given value of f into the value of m which is the second equation and then, solve the value of m.

• 15 + f = m
• 15 + (10) = m
• 25 = m or m = 25

Checking:

Check the values of the variables obtained by substituting to the linear equations in the system.

• f = 10 and m = 25

Equation 1:

• m + f = 35
• (25) + (10) = 35
• 35 = 35 ✔

Equation 2:

• 15 + f = m
• 15 + (10) = (25)
• 25 = 25 ✔

Answer:

∴ Therefore, the number of males is 25 and the number of females is 10 to the class of 35 students.

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