AMC 10 · 2013 · #1
Grade 5 arithmeticPick an answer.
AMC 10 2013 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
This is a rate problem with dollars and miles, so tracking what each number measures keeps the fixed fee separate from the per-mile charge. Splitting the total into a base part and a mileage part turns it into two easy calculations.
Split the cost into two parts
The fare is a flat fee plus a distance charge: $1.50 once, then $0.25 taken 5 times.
The dollars-per-mile only attaches to the miles, so the flat fee has to stand on its own.
The per-mile charge attaches only to the miles, so the flat fee has to stand on its own.
▸ Why?
A rate is quoted for one fixed unit, so it can only be multiplied by a count of those units.
▸ Why?
The fare is exactly the flat fee plus the mileage charge, so the two parts are added, not blended.
Charge for the miles
Multiply the rate by the distance: $0.25 for each of 5 miles makes $1.25 of mileage charge.
Five quarters is $1.25, the same as four quarters plus one more.
5.NBT.B.7Identify SubproblemsAdd the base fare
Add the flat fee to the mileage charge: $1.50 plus $1.25 gives $2.75, which is choice (C).
Line up the cents columns and add: the two amounts combine cleanly to $2.75.
5.NBT.B.7Analyze The UnitsCharge the flat fee once, then add the per-mile rate times the miles.
- Split the cost into two parts
- Charge for the miles
- Add the base fare