AMC 10 · 2011 · #1
Grade 5 arithmeticPick an answer.
The bill is a sum of three independent pieces, so I compute each piece by itself and add them. The pieces mix units (cents, dollars, hours, minutes), so I convert carefully as I go to keep everything in dollars.
Split the bill into three parts
The bill has exactly three parts.
A messy bill becomes easy once you break it into pieces you can price one at a time.
4.OA.A.3Identify SubproblemsCost of the 100 texts
The messages cost 5 in total.
Cost per item times number of items gives the total cost for that item.
5.NBT.B.7Analyze The UnitsHow many extra minutes
Only 30 minutes go past the allowance.
Charges start at the cutoff, so subtract the free amount first, then switch to the unit that gets billed.
Charges start only at the cutoff, so the free allowance comes off before anything is billed.
▸ Why?
The total usage is the free part plus the billed part, so removing one leaves the other.
▸ Why?
Beyond the cutoff each unit costs the same fixed amount, so the bill is a count of units times a price.
Cost of the extra minutes
Those minutes cost 3.
Same idea as the texts: rate times amount gives the cost of that piece.
5.NBT.B.7Analyze The UnitsAdd the three parts
The three parts add to 28, choice (D).
Once every piece is priced in dollars, the total is just their sum.
5.NBT.B.7Identify SubproblemsPrice each part of the bill on its own, remember to bill only the time past the cutoff, then add everything up.
- Split the bill into three parts
- Cost of the 100 texts
- How many extra minutes
- Cost of the extra minutes
- Add the three parts