A delivery drone can carry a payload of at most 27 kilograms. It must always carry a guidance module that weighs 4.2 kilograms. In addition, it carries identical parcels; each parcel adds 1.6 kilograms for its contents and 0.05 kilogram of stabilizing material.
What is the greatest number of parcels the drone can carry on a single trip?
A weight limit that says at most calls for an inequality: the load can reach the limit but cannot exceed it. Add everything that repeats with each parcel, then add equipment carried once. A Desmos regression finds the boundary where the load exactly reaches capacity. Because parcels come in whole numbers, don't round that boundary to the nearest integer.
Hints
- Hint 1
Each parcel adds two weights: its contents and its stabilizing material. Add those first to find the weight of one complete parcel. Which weight is carried only once, no matter how many parcels there are?
- Hint 2
An inequality describes a range of allowed values. The phrase at most means the module and parcels together can weigh 27 kilograms or less. How would you write that limit using ?
- Hint 3
The boundary is the parcel count that would make the load exactly 27 kilograms. Once you find it, remember that must be a whole number. Which whole count stays below the boundary?
Step-by-step
Model the load and find its cutoff
Step 1Find the weight of one parcel
Each parcel has both contents and stabilizing material. Add their weights to get the amount that repeats for every parcel:
- Step 2
Write the weight limit
The guidance module adds kilograms once, and parcels add kilograms. An inequality states the limit:
The means “at most”; an equals sign alone would describe only a full-capacity load.
- Step 3
Find the full-capacity boundary
The boundary is where the load equals kilograms. Type in Desmos; tells it to find . Under PARAMETERS, Desmos shows . Each added parcel raises the weight, so the allowed counts are at or below that boundary.
- Step 4
Choose the greatest whole count
Parcels come in whole numbers. To check the next whole number above the boundary, type on a new Desmos line. It shows kilograms, which exceeds the limit. For a greatest count, move down from an upper cutoff instead of rounding to the nearest integer. The drone can carry parcels on one trip. Grid in 13.