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The school production of Our Town' was a big success. For opening night. 434 tickets were sold. Students paid $4.00 each, while non students paid $6.00 each. If a total of $2032.00 was collected, how many students and how

many non students attended

The number of students was (Simplify your answer)

The number of non-students was (Simplify your answer)

Respuesta :

MrRoyal

Answer:

286 students attended

148 non students attended

Step-by-step explanation:

Given

[tex]Tickets = 434[/tex]

[tex]Students = \$4.00[/tex]

[tex]Non-Students = \$6.00[/tex]

[tex]Total = \$2032.00[/tex]

Solving (a): Number of students

Represent students with S and non students with N

So:

[tex]S + N = 434[/tex] --- (1)

[tex]4S + 6N = 2032[/tex] --- (2)

Make N the subject of formula in (1)

[tex]N = 434 - S[/tex]

Substitute 434 - S for N in (2)

[tex]4S +6(434 - S) = 2032[/tex]

Open Bracket

[tex]4S + 2604 - 6S = 2032[/tex]

Collect Like Terms

[tex]4S - 6S = 2032 - 2604[/tex]

[tex]-2S = -572[/tex]

Divide through by -2

[tex]S = 286[/tex]

Hence; 286 students attended

Solving (b):

Recall that

[tex]N = 434 - S[/tex]

[tex]N = 434 - 286[/tex]

[tex]N = 148[/tex]

148 non students attended

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