AMC 10 · 2011 · #1
Grade 5 arithmeticPick an answer.
AMC 10 2011 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
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 total is the base fee plus the texting cost plus the extra-minutes cost — price each piece, then add.
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
Each text costs 5 cents, or $0.05, so a hundred of them come to $5.00.
Cost per item times number of items gives the total cost for that item.
5.NBT.B.7Analyze The UnitsHow many extra minutes
Only time past 30 hours is billed: 30.5 - 30 = 0.5 hour, which is 30 minutes.
Charges start at the cutoff, so subtract the free amount first, then switch to the unit that gets billed.
4.MD.A.1Analyze The UnitsCost of the extra minutes
Each extra minute costs 10 cents, or $0.10, so 30 of them add $3.00.
Same idea as the texts: rate times amount gives the cost of that piece.
5.NBT.B.7Analyze The UnitsAdd the three parts
Add the three pieces: $20 + $5 + $3 gives $28.00, which is choice (D).
Once every piece is priced in dollars, the total is just their sum.
Once every piece is priced in the same money, the total is just their sum.
▸ Why?
The bill is exactly its parts put together, so nothing is left out of the sum.
▸ Why?
Each part is charged at a fixed rate per unit, so each is a count multiplied by a price.
Price 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