AMC 10 · 2005 · #1
Grade 4 arithmeticPick an answer.
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
Grouping by fives makes the buying total 400.
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
Grouping by twos makes the selling total 500.
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
Subtracting the cost leaves 100, choice (A).
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 a fixed price, so each side of the deal 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