College

Select the correct graph and equation.

A local volunteer group has 150 raffle tickets to sell. They sell them in packs of three tickets per customer. Determine which graph and which equation represent the number of tickets, [tex] T [/tex], the group has left after selling tickets to [tex] c [/tex] customers.

\[
\begin{tabular}{|c|c|}
\hline
\multicolumn{2}{|c|}{Equations} \\
\hline
T = 150c - 3 & T = -3c + 150 \\
\hline
T = -150c + 3 & T = 3c - 150 \\
\hline
\end{tabular}
\]

Answer :

To solve this problem, we need to determine the relationship between the number of raffle tickets the group has left, [tex]\( T \)[/tex], and the number of customers, [tex]\( c \)[/tex], who have each bought a pack of 3 tickets.

1. Identify the initial conditions:
- The group starts with 150 raffle tickets.

2. Determine the sales per customer:
- Each customer buys 3 tickets. So, for each customer [tex]\( c \)[/tex], the group sells [tex]\( 3 \times c \)[/tex] tickets.

3. Set up the equation:
- After selling tickets to [tex]\( c \)[/tex] customers, the number of tickets remaining is the initial number of tickets minus the number sold.
- This can be written as:
[tex]\[
T = 150 - 3c
\][/tex]

4. Match with given equations:
- The equation [tex]\( T = 150 - 3c \)[/tex] is equivalent to [tex]\( T = -3c + 150 \)[/tex] since both represent the same relationship with terms rearranged.

5. Select the correct graph and equation:
- From the table provided, the correct equation that matches our derived equation is:
[tex]\[
T = -3c + 150
\][/tex]

This equation tells us that for every customer who buys a pack of 3 tickets, the number of tickets left decreases by 3, starting from 150.