Answered

Art and his friends spent [tex]\$ 62[/tex] at the movies. Admission tickets cost [tex]\$ 12[/tex] apiece, and a bucket of popcorn costs [tex]\$ 7[/tex]. Which equation written in standard form represents the number of tickets bought, [tex]t[/tex], and the number of buckets of popcorn bought, [tex]p[/tex]?

A. [tex]12t + 7p = 62[/tex]
B. [tex]7t + 12p = 62[/tex]
C. [tex]12p = 62 - 7t[/tex]
D. [tex]7p = 62 - 12t[/tex]



Answer :

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]