Does "no more than" mean the total must be at least $60, or at most $60? Decide whether that corresponds to $\le 60$ or $\ge 60$.

Once you know the correct expression for total cost and which inequality symbol fits the phrase, look for the option that uses both of those correctly.

Let $x$ stand for $c$ (child tickets) and $y$ stand for $a$ (adult tickets). In Desmos, type 8x + 12y on one line to represent the total ticket cost.

Type 8x + 12y <= 60 on one line and 8x + 12y >= 60 on another. Desmos will draw a boundary line and shade one side for each inequality.

Think about combinations like $(x,y) = (3,2)$, which cost $8\cdot3 + 12\cdot2 = 48$ (under $60), and $(5,2)$, which costs $64 (over $60). The correct inequality is the one whose shaded region includes points with total cost $60 or less and excludes points with total cost greater than $60.

Notice that in your Desmos inequalities you used 8x + 12y, which matches the given prices. Any answer choice that has 12c + 8a on the left side does not correctly represent the total cost and should be ruled out.

Each child ticket costs $8, so $c$ child tickets cost $8c$ dollars.

Each adult ticket costs $12, so $a$ adult tickets cost $12a$ dollars.

The total amount the family spends on tickets is the sum of the child-ticket cost and the adult-ticket cost:

$8c + 12a$.

"No more than $60" means the total can be $60 or any smaller amount, but not more.

This is written with the less than or equal to symbol: $\le 60$.

Put the total cost expression together with the inequality from the wording:

$8c + 12a \le 60$.

This matches choice A) $8c + 12a \le 60$.