Question

Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is $55. For one performance, 40 advance tickets and 15 same-day tickets were sold. The total amount paid for the tickets was $1325. What was the price of each kind of ticket?

Answer 1

advance tickets cost $20 each & same-day tickets cost $35 each

Explanation:

Let cost of advanced ticket be x and cost of same-day ticket be y. Now we can write 2 equations and solve them simultaneously.

"The combined cost of one advance ticket and one same-day ticket is $55":

`x+y=55`

and

"...40 advance tickets and 15 same-day tickets were sold. The total amount paid for the tickets was $1325":

`40x+15y=1325`

We solve for x in the first equation to get x = 55 - y and substitute this into 2nd equation and solve for y:

`40(55-y)+15y=1325\\2200-40y+15y=1325\\-25y=1325-2200\\-25y=-875\\y=(-875)/(-25)=35`

Now plugging in y = 35 into the first equation, we can solve for x:

`x+y=55\\x+35=55\\x=55-35\\x=20`

Hence, advance tickets cost $20 each & same-day tickets cost $35 each