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23 votes
23 votes
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?

User Magnus Bull
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1 Answer

18 votes
18 votes

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}

User Goblin
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