Let's solve the problem step-by-step.

Part (a)

We need to write an expression to represent the total cost for two people to go to the movies three times and share a bag of popcorn each time.

1. Cost for movie tickets:

   • The cost for one person to attend one movie is $x$ dollars.
   • Therefore, for two people, it is $2x$ dollars per visit.
   • Since they are going three times, the total cost for the tickets is: $3 \times 2x = 6x$

2. Cost for popcorn:

   • A bag of popcorn costs $4.
   • They buy one bag each time they go to the movies.
   • Since they go three times, the total cost for popcorn is: $3 \times 4 = 12 \text{ dollars}$

3. Total Cost Expression: The total cost $C$ for two people to go to the movies three times and share a bag of popcorn each time is: $C = 6x + 12$

Part (b)

We need to calculate the total cost when the admission is $11 per person (i.e., $x = 11$).

Substitute $x = 11$ into the expression we derived in part (a):

$C = 6(11) + 12$

Calculate:

$C = 66 + 12 = 78$

Final Answers:

• (a) The expression for the total cost is $6x + 12$.
• (b) If the admission is $11 per person, the total cost is $78.

Would you like more details on this solution, or do you have any questions?

Follow-up Questions:

1. What would be the total cost if the price of popcorn changes to $5?
2. How would the expression change if only one person goes to the movies?
3. What if they decide to go to the movies four times instead of three?
4. How would the expression change if the admission cost was different for each visit?
5. What would be the percentage increase in total cost if the movie ticket price increased by 20%?

Tip: When creating expressions for word problems, break down each part to ensure you understand the costs involved for each scenario!