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At a high school football game, admission is $5 for students and $10 for non-students. The school made $4,000 from admissions at the first game,which 500 people attended. How many students and non-students were at the game? Earlier you wrote the system of equations that models thissituation. In this activity, you will solve this system of equations.S+ n = 5005s + 10 = 4,000Part ALooking at the two equations, which method should you use to solve this system of equations?

Respuesta :

[tex]\begin{gathered} s+n=500 \\ 5s+10n=4000 \end{gathered}[/tex]

To solve the system of equation use substitution method:

1. Solve s in the first equation:

[tex]s=500-n[/tex]

2. Substitute in the second equation the s for the value you get in step 1:

[tex]5(500-n)+10n=4000[/tex]

3. Solve n:

[tex]\begin{gathered} 2500-5n+10n=4000 \\ -5n+10n=4000-2500 \\ 5n=1500 \\ n=\frac{1500}{5} \\ \\ n=300 \end{gathered}[/tex]

4. Use the value of n to solve s:

[tex]\begin{gathered} s=500-n \\ s=500-300 \\ s=200 \end{gathered}[/tex]

Then, in the game were 200 students and 300 non-students

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