To determine the correct equation that represents the spending on tickets and popcorn, let's define our variables and understand the problem.
1. Variables:
- [tex]\( t \)[/tex]: The number of tickets bought.
- [tex]\( p \)[/tex]: The number of buckets of popcorn bought.
2. Costs:
- Each ticket costs \[tex]$12.
- Each bucket of popcorn costs \$[/tex]7.
3. Total Spending:
- The total spent was \[tex]$62.
We are asked to find the equation in standard form that correctly represents this situation.
### Setting Up the Equation
The total cost for the tickets and the popcorn can be written as the sum of the individual costs:
- The cost for the tickets: \( 12 \times t \) (since each ticket costs \$[/tex]12 and [tex]\( t \)[/tex] is the number of tickets).
- The cost for the popcorn: [tex]\( 7 \times p \)[/tex] (since each bucket of popcorn costs \[tex]$7 and \( p \) is the number of buckets).
The total cost equation becomes:
\[ 12t + 7p = 62 \]
This equation expresses the relationship between the total cost, the number of tickets, and the number of buckets of popcorn.
### Checking the Given Options
Let's match this setup with the given choices:
1. \( 12p + 7t = 62 \) (This is not correct because it interchanges the variables \( p \) and \( t \)).
2. \( 7p + 12t = 62 \) (This correctly matches our derived equation).
3. \( 12p = 62 - 7t \) (This is a rearranged but not in standard form, and it has the variables interchanged).
4. \( 7p = 62 - 12t \) (This is a rearranged but not in standard form).
The correct equation in standard form that matches our understanding of the problem is:
\[ 7p + 12t = 62 \]
### Conclusion
The equation that represents the number of tickets bought and the number of buckets of popcorn bought, with the total spending of \$[/tex]62, in standard form, is:
[tex]\[ \boxed{7p + 12t = 62} \][/tex]
