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, 20 advance tickets and 35 same-day tickets were sold. The total amount paid for the tickets was $1700. What was the price of each kind of ticket?

Answer 1

Answer:

Price of advance ticket: 15$

Price of same-day ticket: $40

Step-by-step explanation:

Let $y$ be the price of one advance ticket and $x$ the cost of one same day ticket.  

We know that the combined cost of one advance ticket and one same-day ticket is $55, so

$y+x=55$ equation (1)

We also know that 20 advance tickets and 35 same-day tickets cost $1700, so

$20y+35x=1700$ equation (2)

Now, let's solve our system of equations step-by-step:

step 1. Solve for $x$ in equation (1)

$y+x=55$

$x=55-y$ equation (3)

step 2. Replace equation (3) in equation (2)

$20y+35x=1700$

$20y+35(55-y)=1700$

$20y+1925-35y=1700$

$-15y=-225$

$y=\frac{-255}{-15}$

$y=15$ equation (4)

step 3. Replace equation (4) in equation (3)

$x=55-y$

$x=55-15$

$x=40$

We can conclude that the price of one advance ticket is $15 and the price of one same-day ticket is $40.