AMC 10 · 2004 · #1
Grade 4 arithmeticYou and five friends need to raise 1500 dollars in donations for a charity, dividing the fundraising equally. How many dollars will each of you need to raise?
Pick an answer.
AMC 10 2004 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
Try it yourself first — the explanation is most useful after you’ve attempted it.
Toolkit + CCSS Solution
Understand
Restated: You and five friends must raise $1500$ dollars together for charity, and each person raises the same amount. Find how many dollars each person raises.
Givens: The total to be raised is $1500$ dollars.; The fundraising is split equally among everyone.; The group is "you and five friends."; Answer choices: (A) $250$, (B) $300$, (C) $1500$, (D) $7500$, (E) $9000$
Unknowns: The number of dollars each person raises.
Understand
Restated: You and five friends must raise $1500$ dollars together for charity, and each person raises the same amount. Find how many dollars each person raises.
Givens: The total to be raised is $1500$ dollars.; The fundraising is split equally among everyone.; The group is "you and five friends."; Answer choices: (A) $250$, (B) $300$, (C) $1500$, (D) $7500$, (E) $9000$
Plan
Primary tool: #7 Identify Subproblems
Secondary: #3 Eliminate Possibilities
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: $300=1500\div5$ (forgot to count yourself), $1500$ is the whole total undivided, and $7500=1500\times5$ and $9000=1500\times6$ multiply instead of divide.
Execute — Answer: A
4.OA.A.3 Step 1 Count how many people share
- The group is "you and five friends." That is yourself plus $5$ friends, so add them: $1+5=6$.
- Six people are splitting the fundraising, so the total will be divided into $6$ equal shares.
- The easy slip here is reading "five friends" as five people total and forgetting to count yourself.
💡 "You and five friends" always includes you, so the sharing group is one bigger than the number of friends.
4.NBT.B.6 Step 2 Divide the total into equal shares
- The $1500$ dollars is split equally among the $6$ people, so each person's share is $1500\div6$.
- Since $6\times25=150$, it follows that $6\times250=1500$, so $1500\div6=250$.
- Each person raises $250$ dollars.
💡 Splitting a total into equal shares is division: total money divided by number of people gives one share.
4.OA.A.3 Step 3 Rule out the trap choices
- Each share is $250$ dollars, which is choice (A).
- The other choices are each a specific mistake: $300$ (B) is $1500\div5$, from forgetting to count yourself; $1500$ (C) is the whole total, not divided at all; and $7500$ (D) and $9000$ (E) multiply ($1500\times5$ and $1500\times6$) instead of dividing, which would make the group raise far more than the target.
- Only dividing by the correct count of $6$ gives $250$, so the answer is (A).
💡 Sharing makes each person's amount smaller than the total, so the answer must be well below $1500$.
4.OA.A.3 The group is "you and five friends." That is yourself plus $5$ friends, so add t 4.NBT.B.6 The $1500$ dollars is split equally among the $6$ people, so each person's share 4.OA.A.3 Each share is $250$ dollars, which is choice (A). The other choices are each a s Review
Reasonableness: A share must be smaller than the whole $1500$, which immediately kills $1500$ (C), $7500$ (D), and $9000$ (E) — you cannot each raise as much as, or more than, the entire goal. That leaves $250$ and $300$. Checking the count: $6$ people at $250$ dollars is $6\times250=1500$, exactly the target, while $6$ people at $300$ would be $1800$, too much. So $250$ (A) is right.
Alternative: Work backwards from the choices (Tool #11): test each amount by multiplying it by the $6$ people and see which hits $1500$. Only $250\times6=1500$ lands on the goal; $300\times6=1800$ overshoots. This confirms (A) without doing the long division directly.
CCSS standards used (min grade 4)
4.OA.A.3Solve multi-step word problems using four operations with whole numbers (Reading "you and five friends" as 6 people and checking each answer choice against that count.)4.NBT.B.6Find whole-number quotients and remainders with up to four-digit dividends (Computing $1500\div6=250$, the equal share each person raises.)
⭐ When a group shares a total equally, count everyone — including yourself — then divide the total by how many people there are.
⭐ When a group shares a total equally, count everyone — including yourself — then divide the total by how many people there are.
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