Tickets for the homecoming dance cost $20 for a single ticket or $35 for a couple. Ticket sales totaled $2280, and 128 people attended. How many tickets of each type were sold?

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Answer 1 · 2018-03-20T21:29:26

#16# singles, #56# couples

There's two linear equations that we can make: one for money and one for people.

Let the number of single tickets be #s# and the number of couple tickets be #c#.

We know that the amount of money we make is
#$ = 20 s + 35 c = 2280#

We also how many people can come
#P = 1 s + 2 c = 128 #

We know that both #s# are the same and both #c# are the same. We have two unknowns and two equations, so we can do some algebra to solve for each.

Take the first minus twenty times the second:
#20 s + 35 c = 2280 #
#-20 s - 40 c = -2560 #
#-5c = -280 implies c = 56 #

Plugging this back into the second equation,
#s + 2c = s + 2 * 56 = s + 112 = 128 implies s = 16 #