Question

Three tickets to attend an Off-Broadway show cost $81, 4 tickets cost $108, and 5 tickets cost $135. Show that the relationship between number and the cost is a proportional relationship by making a table of tickets for 1 to 5 tickets. Show your work. Number of Tickets 1 2 3 4 5 Total Cost ($) What is the constant of proportionality, k? Write and Equation for the relationship. (Remember to state what the variables represent)

Answer 1

• k=27
• y=27x

Explanation:

3 tickets to attend an Off-Broadway show cost $81,

4 tickets cost $108; and

5 tickets cost $135.

Let the price of a ticket=k

Therefore:

• 3k=81
• 4k=108
• 5k=135

Solving any of the equation above gives: x=27

We therefore have:

`\left|\begin{array}c$Tickets&1&2&3&4&5\\$Total Cost(\$)&27&54&81&108&135\end{array}\right|`

Let y be the total cost of x tickets

• From the above, the constant of proportionality, k=27

An equation for the relationship is therefore:

y=27x (where x is the number of tickets and y is the total costs (in $)).