Ms. Chapman wants to take her scout troop to Neon Nights roller rink. The employee she spoke to ahead of time said the total cost for all 9 people in the group would be $81. This includes an entrance ticket and a $3 skate rental fee for each person.
Which equation can you use to find $t$, the cost of each entrance ticket?
$3(t+9)=81$
$9(t+3)=81$
$3 t+9=81$
$9 t+3=81$
How much does each entrance ticket cost?
$ \square
Answer (1)
Set up the equation representing the total cost: 9 t + 27 = 81 .
Simplify the equation by subtracting 27 from both sides: 9 t = 54 .
Solve for t by dividing both sides by 9: t = 6 .
The cost of each entrance ticket is 6 .
Explanation
Understanding the Problem Let's break down the problem. We know the total cost for 9 people is 81. E a c h p erso nn ee d s an e n t r an ce t i c k e t , w hi c h cos t s t$, and skate rentals, which cost 3. S o , w e n ee d t o f in d an e q u a t i o n t ha t re p rese n t s t hi ss i t u a t i o nan d t h e n so l v e f or t$.
Setting up the Equation The total cost is the sum of the cost of entrance tickets for 9 people and the cost of skate rentals for 9 people. The cost of entrance tickets for 9 people is 9 t . The cost of skate rentals for 9 people is 9 × 3 = 27 . So the total cost can be represented as 9 t + 27 = 81 . Therefore, the correct equation is 9 ( t + 3 ) = 81 .
Solving for t Now, let's solve the equation 9 t + 27 = 81 for t . First, we subtract 27 from both sides of the equation: 9 t = 81 − 27 9 t = 54 Then, we divide both sides by 9: t = 9 54 t = 6
Finding the Cost So, the cost of each entrance ticket is $6.
Examples
Imagine you're organizing a field trip for your class to a museum. You need to figure out the cost per student, knowing the total expense includes entrance fees and a fixed transportation cost. This problem is similar; by setting up an equation, you can determine the individual cost of each ticket. For instance, if the total cost for 25 students is $500 , and the transportation cost is $100 , you can calculate the entrance fee per student. This kind of problem-solving is useful in budgeting and planning various events, ensuring you can accurately determine individual costs within a group.
