Ticket Question

Question

Mr. Tom decided to sell tickets for a special event being held at the school. He sold 10 more adult tickets than child tickets. He sold twice as many youth tickets as child tickets.

a) Create an algebraic expression you could use to determine the total number of tickets he sold.

b) Adult tickets cost $5. Children’s tickets cost $2. Youth tickets cost $3. He made $700. How many tickets did he sell for the event?

c) For another event, only youth tickets were being sold. How many tickets would need to be sold in order to make a profit if the DJ for the event was going to cost $550?

Answer 1

Here's what we know:

a = c +10 (there were 10 more adult tickets than child sold)

y = 2c (there were twice as many youth tickets than child sold)

(a)

to create an expression, the most basic would be a + c + y, as those would be the three types of tickets sold, but we can also put in the known values for the variables:

c + 10 + c + 2c

Simplify that for another expression.

(b)

Start by taking the first expression, and adding the prices as the coefficients, and the 700 as the total:

5a + 2c + 3y = 700

Now place in the known values for the variables:

5(c + 10) + 2c + 3(2c) = 700

Distribute:

5c + 50 + 2c + 6c = 700

Simplify:

13c + 50 = 700

Isolate c:

13c = 650

c = 50

Now that you know c, you can use that to find a and y.

(c)

We're looking for an inequality because we want a profit here. Youth tickets cost $3 and the event costs $550:

3y > 550

Isolate y to get your answer. (Remember, you cannot sell part of a ticket)