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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.
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.
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