Art and his friends spent $62 at the movies. Admission tickets cost $12 apiece, and a bucket of popcorn costs $7. Which equation written in standard form represents the number of tickets bought, $t$, and the number of buckets of popcorn bought, $p$?
A. $12p+7t=62$
B. $7p+12t=62$
C. $12p=62-7t$
D. $7p=62-12t
Answer (2)
The total cost of tickets is 12 t .
The total cost of popcorn is 7 p .
The sum of the costs equals the total amount spent: 12 t + 7 p = 62 .
The equation in standard form is 7 p + 12 t = 62 .
Explanation
Understanding the Problem We are given that Art and his friends spent a total of $62 at the movies. The cost of each admission ticket is $12, and the cost of each bucket of popcorn is $7. We need to find the equation that represents the number of tickets bought, denoted by t , and the number of buckets of popcorn bought, denoted by p .
Formulating the Equation The total cost of the tickets is the cost per ticket multiplied by the number of tickets, which is 12 t . The total cost of the popcorn is the cost per bucket multiplied by the number of buckets, which is 7 p . The sum of these costs must equal the total amount spent, which is $62. Therefore, the equation is: 12 t + 7 p = 62
Matching the Equation The equation 12 t + 7 p = 62 is already in standard form, where the variables t and p are on one side of the equation and the constant is on the other side. Comparing this equation with the given options, we see that it matches the second option when the terms are rearranged.
Final Answer The equation representing the number of tickets bought, t , and the number of buckets of popcorn bought, p , is 12 t + 7 p = 62 . This can also be written as 7 p + 12 t = 62 .
Examples
Imagine you're planning a school carnival. Tickets for games cost $3 each, and snacks are $2 each. You have a budget of $30. The equation 3t + 2s = 30 helps you figure out how many game tickets (t) and snacks (s) you can buy without exceeding your budget. This kind of equation is useful for budgeting and making sure you stay within your financial limits.
The equation representing the total costs of tickets and popcorn spent by Art and his friends is 7 p + 12 t = 62 . This reflects the cost of admission tickets at $12 each and popcorn at $7 each. The correct option is B.
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