Gwen volunteered to work at the ticket booth for her school's Halloween carnival. The chart below gives the number of hours Gwen worked and the total number of tickets she sold.

Question

Hours (h) Tickets (t)
Hours (h): 1 Tickets (t): 23
Hours (h): 2 Tickets (t): 46
Hours (h): 3 Tickets (t): 69
Hours (h): 4 Tickets (t): 92
Based on the table, write an equation for the relation between the number hours Gwen worked and the number of tickets she sold.

Answer 1

To determine the equation that relates the number of hours Gwen worked (h) to the number of tickets she sold (t), we can observe the pattern in the provided data:

• For every hour (h) Gwen worked, she sold 23 tickets (t).
• The relationship can be expressed with a linear equation in the form of \( t = mh + b \), where \( m \) is the slope and \( b \) is the y-intercept.

From the data:

• When \( h = 1 \), \( t = 23 \)
• When \( h = 2 \), \( t = 46 \)
• When \( h = 3 \), \( t = 69 \)
• When \( h = 4 \), \( t = 92 \)

We can see that for every additional hour worked, the number of tickets sold increases by 23. Therefore, the slope \( m \) is \( 23 \).

Since when \( h = 0 \) (no hours worked), we would expect \( t = 0 \) (no tickets sold), the y-intercept \( b \) is 0.

Putting this together, the equation relating the number of hours Gwen worked to the number of tickets she sold is:

\[ t = 23h \]

This equation accurately represents the data provided in the chart.