Question

a math class has a total of 38 students. The number of females is 16 less than the number of males. How many males and how many females are in class?

Answer 1

Write the system of equations.

let x be number of male students

let y be number of female students

the number of students can be modeled by the equation

`x+y=38`

the number of female students can be modeled by the equation

`y=x-16`

insert the second equation into the first equation

`\begin{gathered} x+(x-16)=38 \\ 2x-16=38 \end{gathered}`

solve the equation for x

`\begin{gathered} 2x=38+16 \\ 2x=54 \\ x=(54)/(2) \\ x=27 \end{gathered}`

use the number of x into the second equation to find y

`\begin{gathered} y=x-16 \\ y=27-16 \\ y=11 \end{gathered}`

prove that the results is correct with the first equation

`\begin{gathered} x+y=38 \\ 27+11=38 \\ 38=38 \end{gathered}`