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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.

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

Answer :

To determine which equation represents the number of tickets, [tex]\( T \)[/tex], the group has left after selling tickets to [tex]\( C \)[/tex] customers, let's break down the problem:

1. Understand the Problem:
- The group starts with a total of 150 raffle tickets.
- Each customer buys a pack of 3 tickets.

2. Determine the Total Tickets Sold to [tex]\( C \)[/tex] Customers:
- If each customer buys 3 tickets, then after serving [tex]\( C \)[/tex] customers, the group will have sold [tex]\( 3C \)[/tex] tickets in total.

3. Write the Expression for Tickets Left:
- The number of tickets left, [tex]\( T \)[/tex], is the initial number of tickets minus the number of tickets sold.
- Therefore, the equation becomes:
[tex]\[
T = 150 - 3C
\][/tex]

4. Match with Given Options:
- From the options given, we look for an equation that matches [tex]\( T = 150 - 3C \)[/tex], which can also be written as [tex]\( T = -3C + 150 \)[/tex].

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

This matches the equation [tex]\( T = -3C + 150 \)[/tex] from the provided table. As a result, this is the correct representation of the situation.

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