To determine which equation in standard form represents the number of tickets bought, [tex]\( t \)[/tex], and the number of buckets of popcorn bought, [tex]\( p \)[/tex], let's look at the problem step by step:
1. Identify the costs:
- The cost of one admission ticket is [tex]\( \$12 \)[/tex].
- The cost of one bucket of popcorn is [tex]\( \$7 \)[/tex].
2. Set up the total cost equation:
- The total amount of money spent is [tex]\( \$62 \)[/tex].
3. Formulate the equation:
- Given that the cost of each ticket is [tex]\( \$12 \)[/tex], if [tex]\( t \)[/tex] represents the number of tickets, the total cost for tickets is [tex]\( 12t \)[/tex].
- Given that the cost of each bucket of popcorn is [tex]\( \$7 \)[/tex], if [tex]\( p \)[/tex] represents the number of buckets of popcorn, the total cost for popcorn is [tex]\( 7p \)[/tex].
4. Combine the costs:
- We need to combine the costs of tickets and popcorn to equal the total amount spent, which is [tex]\( \$62 \)[/tex].
So, the equation becomes:
[tex]\[ 12t + 7p = 62 \][/tex]
5. Match the correct equation:
- Now, let's compare this with the given options:
- [tex]\( 12p + 7t = 62 \)[/tex]
- [tex]\( 7p + 12t = 62 \)[/tex]
- [tex]\( 12p = 62 - 7t \)[/tex]
- [tex]\( 7p = 62 - 12t \)[/tex]
The equation [tex]\( 12t + 7p = 62 \)[/tex] matches the second option [tex]\( 7p + 12t = 62 \)[/tex].
Therefore, the correct equation that represents the number of tickets bought, [tex]\( t \)[/tex], and the number of buckets of popcorn bought, [tex]\( p \)[/tex], is:
[tex]\[ \boxed{2} \][/tex]
