# 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? ##### 1 Answer Mar 20, 2018 $16$singles, $56$couples #### Explanation: 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:
$20 s + 35 c = 2280$
$- 20 s - 40 c = - 2560$
$- 5 c = - 280 \implies c = 56$

Plugging this back into the second equation,
$s + 2 c = s + 2 \cdot 56 = s + 112 = 128 \implies s = 16$