How is the linear system?

Question

Tickets for the school play cost $4 for adults and $2 for students. At the end of the play, our school sold a total of 105 tickets and collected $360. Write a linear system to find out the number of adult tickets sold and the number of student tickets sold

Answer 1

All of the tickets added together, adult and student, gives 105 tickets. So,

 

a + s = 105   is our first equation in the system

 

In terms of dollars per ticket: adults = 4a and students = 2s

 

4a + 2s = 360  is our second equation

 

Use the first equation to get one variable by itself (I chose to have "a" by itself).

a = 105 - s      and substitute this into the second equation

 

4(105 - s) + 2s = 360     Substitute

420 - 4s + 2s = 360        Combine like terms

420 - 2s = 360                subtract 420 from each side

-2s = -60                       Divide by -2 from each side

s = 30***                      Substitute into the original equation to find "a"

a + 30 = 105                 Subtract 30 from each side

a = 75***                     Check your answers

 

4(75) + 2(30) = 360

300 + 60 = 360

360 = 360

 

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