AMC 10 · 2004 · #1
Easy mode Grade 4You and five friends are raising money for a charity. Together the whole group needs to collect 1500 dollars, and everyone raises the same amount. How many dollars does each person 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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