The large cartons are 4 times the number of medium cartons. Once you have an expression for the number of medium cartons, how do you write the number of large cartons?

Add your expressions for small, medium, and large cartons to represent the total number of cartons, and then set that sum equal to 222. Simplify the left side and compare it to the answer choices.

In Desmos, type the expression for the total number of cartons in terms of $s$:

T(s) = s + (s + 9) + 4(s + 9)

Desmos will automatically simplify this expression into a linear expression of the form a s + b.

Look at the simplified form that Desmos shows for T(s) and then set that expression equal to 222. Compare this equation to the answer choices and select the one whose left-hand side matches the simplified expression from Desmos.

Let $s$ represent the number of small cartons.

• Medium cartons: The problem says the number of medium cartons was 9 more than the number $s$ of small cartons, so the number of medium cartons is $s+9$.
• Large cartons: The number of large cartons was 4 times the number of medium cartons, so the number of large cartons is $4(s+9)$.

Add the expressions for small, medium, and large cartons to get the total number of cartons in terms of $s$:

• Small: $s$
• Medium: $s+9$
• Large: $4(s+9)$

So the total is

The problem states that altogether, the warehouse prepared 222 cartons. That means the total expression from the previous step must equal 222:

Now combine like terms on the left side:

• Combine the $s$ terms: $s + s + 4s = 6s$.
• Combine the constant terms: $9 + 4\cdot 9 = 9 + 36 = 45$.

So the left side becomes $6s + 45$.

From the simplification, the relationship between $s$ and the total number of cartons is

This matches choice D, so $6s + 45 = 222$ is the correct equation representing the situation.