AMC 10 · 2005 · #1
Grade 4 arithmeticPick an answer.
AMC 10 2005 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
Both prices are quoted per group of bars, not per single bar, so Tool #8 (Analyze the Units) keeps the two units straight: how many groups of bars, and how many dollars each group is worth. Tool #7 (Identify Subproblems) splits the work into three clean pieces — money spent buying, money taken in selling, then the difference. Tool #3 (Eliminate Possibilities) guards the main trap: choice (E) 500 is exactly the selling total, which is what you get if you forget to subtract the buying cost.
Money spent buying
Bought five at a time, 1000 bars make 1000÷5=200 groups at 2 dollars each, so buying costs 400 dollars.
Count how many price-groups the bars make, then pay the group price that many times.
4.NBT.B.6Analyze The UnitsMoney taken in selling
Sold two at a time, 1000 bars make 1000÷2=500 pairs at 1 dollar each, so selling brings in 500 dollars.
Same idea as buying, but now the group is a pair and each pair brings in a dollar.
4.NBT.B.6Analyze The UnitsProfit is selling minus buying
Profit is money in minus money out: 500-400=100 dollars, choice (A) — not the 500 taken in.
Profit is what stays in your pocket after you pay back what you spent.
Profit is what stays after the money paid out is taken back from the money taken in.
▸ Why?
Bars are bought and sold in fixed-size bundles at fixed prices, so each side is a count of bundles times a price.
▸ Why?
The money taken in is the money paid out plus the profit, so removing one part leaves the other.
Turn a per-group price into a total by counting the groups, then remember profit is what you sell for minus what you paid — not just the money you took in.
- Money spent buying
- Money taken in selling
- Profit is selling minus buying