Each parcel has 1.6 kg of contents and 0.05 kg of stabilizing material. Combine these into a single number that represents the weight of one parcel.

Use a $\le$ inequality to show that the total weight (module + $n$ parcels) must be at most 27 kg, then solve that inequality for $n$.

Your solution for $n$ might not be a whole number. Since $n$ is a number of parcels, what should you do with a non-integer solution to find the greatest possible $n$?

In Desmos, type W(n) = 4.2 + (1.6 + 0.05)*n to define the total payload weight (in kilograms) as a function of the number of parcels $n$.

Desmos will offer to create a slider for n. Accept it, and set the slider range to go from 0 to about 30 so you can test different parcel counts.

Slowly increase the value of n using the slider and watch the value of W(n). Look for the greatest integer value of n for which W(n) is still less than or equal to 27; the next integer up will make W(n) exceed 27.

The drone can carry at most 27 kg. That means the total weight (guidance module + all parcels) must satisfy an inequality using $\le$ ("less than or equal to"):

• Guidance module: $4.2$ kg (always there)
• Each parcel: $1.6$ kg contents $+$ $0.05$ kg stabilizing material

So each parcel weighs $1.6 + 0.05$ kg, and with $n$ parcels the total payload weight is:

First combine the weights that belong together.

Each parcel:

So the inequality becomes:

Isolate $n$ step by step.

Subtract $4.2$ from both sides:

Now divide both sides by $1.65$ (a positive number, so the inequality direction stays the same):

Compute $\frac{22.8}{1.65}$ to get a decimal value for $n$. Don’t round yet; think about what it means for the number of parcels.

Evaluating the division gives a value a bit less than $14$.

Because $n$ is a number of parcels, it must be a whole number and must still satisfy $4.2 + 1.65n \le 27$.

• Check $n = 14$: the total weight is more than $27$ kg, so this is too many parcels.
• The largest integer less than this cutoff that still fits within 27 kg is $\boxed{13}$.