Question

Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $25 and same-day tickets cost

$40. For one performance, there were 40 tickets sold in all, and the total amount paid for them was $1225. How many tickets of
each type were sold?

Answer 1

Let x be the number of advance tickets sold and y be the number of same-day tickets sold.
We know that x + y = 40 (the total number of tickets sold) and 25x + 40y = 1225 (the total amount paid for the tickets).

We can use the first equation to solve for one of the variables in terms of the other:
x = 40 - y

We can substitute this expression into the second equation to get:
25(40 - y) + 40y = 1225
1000 - 25y + 40y = 1225
-25y + 40y = 225
15y = 225
y = 15

So 15 same-day tickets were sold.

Now we can substitute this value back into the first equation to find the number of advance tickets sold:
x + 15 = 40
x = 25

So 25 advance tickets were sold.