AMC 10 · 2009 · #2
Grade 6 rate-ratioPick an answer.
The whole problem hinges on one hidden rate: how much paint one room takes, measured in cans per room. Tool #8 (Analyze the Units) puts that rate at the center — once we know cans per room, the 25-room total is one multiplication. Tool #7 (Identify Subproblems) sets it up in stages: first turn the lost cans into a number of lost rooms, then find the per-room rate, then scale up to 25 rooms.
Turn the lost cans into lost rooms
The lost cans equal the lost rooms in paint.
Whatever was lost is just the gap between what she could paint before and after.
4.OA.A.3Identify SubproblemsFind the paint per room
Dividing gives the paint per room.
Splitting the cans evenly among the rooms they cover gives the cost of a single room.
Splitting the cans evenly among the rooms they cover gives the cost of a single room.
▸ Why?
Sharing a total among equal rooms gives each room an equal share of it.
▸ Why?
With the paint per room fixed, any number of rooms is that amount repeated.
Scale up to 25 rooms
Scaling up gives 15, choice (C).
Once you know the cost of one room, any number of rooms is just repeated copies of that cost.
5.NF.B.4Analyze The UnitsFind how much paint one room needs first; then any number of rooms is just that amount multiplied up.
- Turn the lost cans into lost rooms
- Find the paint per room
- Scale up to 25 rooms