AMC 10 · 2004 · #1
Grade 4 arithmeticPick an answer.
AMC 10 2004 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The problem breaks into two clean subproblems (Tool #7): first figure out how many people are sharing the work, then divide the 1500 dollars by that count. The one real trap is the head-count — "you and five friends" is 6 people, so dividing by 5 instead of 6 is the mistake every wrong answer is built on. Tool #3 (Eliminate Possibilities) turns each wrong choice into a named error: 300=1500÷5 (forgot to count yourself), 1500 is the whole total undivided, and 7500=1500×5 and 9000=1500×6 multiply instead of divide.
Count how many people share
"You and five friends" is yourself plus 5 friends, so 6 people share the total — not 5.
"You and five friends" always includes you, so the sharing group is one bigger than the number of friends.
You and five friends always includes you, so the sharing group is one bigger than the number of friends.
▸ Why?
Each person in the group is counted exactly once, and the speaker is one of them.
▸ Why?
The group is exactly the speaker plus the friends, so the counts add.
Divide the total into equal shares
Split 1500 among the 6 people: since 6×250=1500, each share is 250 dollars.
Splitting a total into equal shares is division: total money divided by number of people gives one share.
4.NBT.B.6Identify SubproblemsRule out the trap choices
Only 250 survives: (B) 300 divides by 5, (C) 1500 never divides, (D) and (E) multiply — so (A).
Sharing makes each person's amount smaller than the total, so the answer must be well below 1500.
4.OA.A.3Eliminate PossibilitiesWhen a group shares a total equally, count everyone — including yourself — then divide the total by how many people there are.
- Count how many people share
- Divide the total into equal shares
- Rule out the trap choices