Question

Tickets for a high school dance cost $1.00 each of purchased in advance of the dance, but $1.50 each if bought at the door. If 100 tickets were sold and $120 was collected, how many tickets were sold in advance and how many were sold at the door?

Answer 1

Answer:

Tickets were sold in advance are 60 and the tickets were sold at the door are 40.

Step-by-step explanation:

Given:

Tickets for a high school dance.

Cost $1.00 each of purchased in advance of the dance.

Cost $1.50 each if bought at the door.

100 tickets were sold and $120 was collected.

Now, to find the tickets that were sold in advance and sold at the door.

Let the number of tickets sold in advance be $x$.

And the number of tickets sold at the door be $y$.

So, the total number of tickets sold:

$x+y=100.$

$y=100-x.$......(1)

Now, the total amount collected:

$1.00x+1.50y=120.$

Putting the equation (1) in the place of $y$ we get:

$1x+1.5(100-x)=120$

$1x+150-1.5x=120$

$150-0.5x=120$

Adding both sides by $0.5x$ we get:

$150=120+0.5x$

Subtracting both sides by 120 we get:

$30=0.5x$

Dividing 0.5 by both sides we get:

$60=x$

Thus, the number of tickets sold in advance = 60.

Putting the value of $x$ in equation (1) we get:

$y=100-60$

$y=40.$

So, the number of tickets sold at the door = 40.

Therefore, tickets were sold in advance are 60 and tickets were sold at the door are 40.