High School

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.

Equations:

[tex]\[
\begin{array}{ll}
A. & T = 150c - 3 \\
B. & T = -3c + 150 \\
C. & T = -150c + 3 \\
D. & T = 3c - 150 \\
\end{array}
\][/tex]

Answer :

To solve this problem, we need to determine how the number of tickets left, [tex]\( T \)[/tex], changes as the group sells the tickets in packs of three to each customer, [tex]\( c \)[/tex]. Here's how you can think about it step-by-step:

1. Initial Number of Tickets: The local volunteer group starts with 150 raffle tickets.

2. Tickets Sold per Customer: They sell tickets in packs of three, meaning each customer buys 3 tickets.

3. Equation Setup:
- When one customer buys, the group has fewer tickets, specifically 3 fewer than before.
- Therefore, for [tex]\( c \)[/tex] customers, the group will have sold [tex]\( 3c \)[/tex] tickets in total.

4. Equation for Tickets Left:
- Initially, there are 150 tickets.
- After selling tickets to [tex]\( c \)[/tex] customers, they have [tex]\( 150 - 3c \)[/tex] tickets remaining.
- So, the equation representing this situation is: [tex]\( T = 150 - 3c \)[/tex].

5. Matching with Given Options:
- Comparing [tex]\( T = 150 - 3c \)[/tex] with the given options:
- [tex]\( T = 150c - 3 \)[/tex]
- [tex]\( T = -3c + 150 \)[/tex]
- [tex]\( T = -150c + 3 \)[/tex]
- [tex]\( T = 3c - 150 \)[/tex]
- The correct matching equation is [tex]\( T = -3c + 150 \)[/tex].

Therefore, the correct equation that represents the number of tickets left after selling tickets to [tex]\( c \)[/tex] customers is [tex]\( T = -3c + 150 \)[/tex]. This equation fits the conditions the group faces as they sell their tickets.