AMC 10 · 2006 · #1
Grade 3 arithmeticPick an answer.
AMC 10 2006 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
This is a money problem where each item has a price in dollars-per-item, so Tool #8 (Analyze the Units) says: multiply how many by the price each to get dollars. Tool #7 (Identify Subproblems) splits the order into two easy pieces — the cost of the sandwiches and the cost of the sodas — which are then added. Tool #3 (Eliminate Possibilities) gives a fast reality check: the choices are all near 30, and the two subtotals are 15 and 16, so the answer must sit at the low end.
Cost of the sandwiches
Five sandwiches at $3 each is 5 equal groups of 3, so multiply: the sandwiches come to $15.
Same price repeated is just multiplication: how many times how much each.
3.OA.A.3Analyze The UnitsCost of the sodas
Eight sodas at $2 each is 8 equal groups of 2, so the sodas come to $16.
Count the sodas, multiply by the price each, and you have their share of the bill.
3.OA.A.3Analyze The UnitsAdd the two subtotals
The whole bill is the two parts added, so $15 + $16 = $31 — choice (A), and far too small for (D) or (E).
The total bill is simply every part of the order added together.
The whole bill is every part of the order added together.
▸ Why?
The same price repeated is a count of equal groups, which is exactly what multiplying records.
▸ Why?
The order is made of its parts and nothing else, so their totals add up to the total.
For a shopping bill, multiply each item's count by its price, then add the pieces together.
- Cost of the sandwiches
- Cost of the sodas
- Add the two subtotals