Look at the phrase "no more than $60". Does that mean the total cost should be greater than, less than, or equal to 60? Think about which inequality symbol matches "no more than."

Each child ticket is $6 and each adult ticket is $10. How do you combine $c$ and $a$ with these prices to get an expression for the total cost in dollars?

Once you have one inequality for the total number of tickets and another for the total cost, write them as a system and then look for the answer choice that has both of those inequalities together.

In Desmos, use $x$ for child tickets and $y$ for adult tickets (Desmos expects $x$ and $y$ as the default variables). For example, wherever you see $c$ in an answer choice, think $x$, and wherever you see $a$, think $y$.

For each option (A, B, C, and D), type its two inequalities into Desmos, replacing $c$ with $x$ and $a$ with $y$. Desmos will shade the region that satisfies both inequalities in that choice.

For each shaded region, ask:

• Does every point in the region have a total number of tickets $x + y$ that is at least 5?
• Does every point in the region have a total cost $6x + 10y$ that is no more than 60? If the region allows fewer than 5 tickets or costs greater than 60, eliminate that option.

After checking all four options in Desmos, identify which system’s shaded region always represents combinations with at least 5 tickets and a total cost of at most $60. The corresponding letter is your answer.

Let $c$ be the number of child tickets and $a$ be the number of adult tickets.

The group must buy at least 5 tickets in total. The total number of tickets is $c + a$.

• "At least 5" means 5 or more, so we use $\ge$.
• This gives the inequality: $c + a \ge 5$.

This handles the ticket-count condition only.

Child tickets cost $6 each and adult tickets cost $10 each.

• The cost from child tickets is $6c$.
• The cost from adult tickets is $10a$.

So the total cost is represented by the expression $6c + 10a$.

The group wants to spend no more than $60.

• "No more than 60" means the amount is less than or equal to 60.
• Using the total cost expression $6c + 10a$, we write:

This inequality captures the cost restriction.

Now put the two inequalities together:

• Ticket count: $c + a \ge 5$
• Cost: $6c + 10a \le 60$

So the system that models the situation is

Comparing with the answer choices, this matches choice D.