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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.
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.
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