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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 the problem, we need to find out which equation correctly represents the number of tickets, [tex]\( T \)[/tex], the group has left after selling tickets to [tex]\( c \)[/tex] customers. Let's go through the steps:

1. Understand the Problem:
- The group starts with a total of 150 tickets.
- They sell tickets in packs of 3 tickets per customer.

2. Determine the Reduction in Tickets:
- For each customer, 3 tickets are sold. Hence, if there are [tex]\( c \)[/tex] customers, the total number of tickets sold is [tex]\( 3c \)[/tex].

3. Calculate Tickets Left:
- Start with the total number of tickets, 150.
- Subtract the number of tickets sold, which is [tex]\( 3c \)[/tex].
- The equation to find the number of tickets left, [tex]\( T \)[/tex], becomes:
[tex]\[
T = 150 - 3c
\][/tex]

4. Identify the Correct Equation:
- From the provided options, the equation [tex]\( T = -3c + 150 \)[/tex] correctly represents the scenario.

Thus, the correct equation that represents the number of tickets left after selling tickets to [tex]\( c \)[/tex] customers is:
[tex]\[ T = -3c + 150 \][/tex]

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