AMC 10 · 2006 · #5
Grade 5 arithmeticPick an answer.
The whole question is really about dollars-per-slice, so Tool #8 (Analyze the Units) drives it: find the cost of one plain slice and one anchovy slice. Tool #7 (Identify Subproblems) then handles each eater separately — add up Dave's slices, add up Doug's slices. Tool #3 (Eliminate Possibilities) keeps the arithmetic honest: the two payments must still add to the $10 total, which flags any slip.
Price one plain slice
A plain slice carries 1.
Equal slices split the plain bill evenly, so each one is worth its fair share of the $8.
5.NF.B.3Analyze The UnitsPrice one anchovy slice
The extra spreads over only the topped half, so such a slice costs more.
The topping charge belongs only to the slices that actually got anchovies, so split it just among those four.
The topping charge belongs only to the slices that actually got anchovies, so it is split just among those four.
▸ Why?
Splitting a charge among equal slices gives each one an equal share of it.
▸ Why?
The topping is bought once for a fixed set of slices, so its price attaches to that set and no other.
Add up what Dave ate
The first person's slices total 7.
Charge Dave for each slice he ate at that slice's own price, then total it.
5.NBT.B.7Identify SubproblemsAdd up Doug's share and compare
The two totals add back to the full bill, and the gap is 4, choice (D).
Doug only ever ate plain slices, so his bill is just the plain price times how many he ate.
4.OA.A.3Identify SubproblemsFind the price of each kind of slice first, put the anchovy charge only on the slices that got anchovies, then charge each person for exactly what he ate.
- Price one plain slice
- Price one anchovy slice
- Add up what Dave ate
- Add up Doug's share and compare