Tickets for your schools play are $3 for students and $5 for non-students. On opening night 937 tickets are sold & $3943 is collected. How many tickets were sold to students and non students?

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Answer 1 · 2015-08-06T18:53:52

The school sold 371 tickets for students and 566 tickets for non-students.

Let's say that the number of tickets sold to students is #x# and the number of tickets sold to non-students is #y#.

You know that the school sold a total of 937 tickets, which means that you can write

#x + y = 937#

You also know that the total sum collected from selling these tickets is equal to $3943, so you can write

#3 * x + 5 * y = 3943#

Use the first equation to write #x# as a function of #y#

#x = 937 - y#

Plug this into the second equation and solve for #y# to get

#3 * (937 - y) + 5y = 3943#

#2811 - 3y + 5y = 3943#

#2y = 1132 implies y = 1132/2 = color(green)("566 tickets")#

This means that #x# will be equal to

#x = 937 - 566 = color(green)("371 tickets")#

The school thus sold 371 tickets for students and 566 tickets for non-students.