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2004 AMC 10A Problem 1

2004 AMC 10A Problem 1AMC 10 Step by Step

Name: Date: October 28, 2026

Linear Equations & Word Problems · difficulty 1 of 5 · about 1 min · position P1-10

You 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?

A) $250$
B) $300$
C) $1500$
D) $7500$
E) $9000$

Answer

Key insight

Count the people first. You plus five friends is six people, so each person raises 1500 divided by 6.

Solution

1. Count who is raising money. It is you plus five friends, so $1 + 5 = 6$ people.
2. The total is shared equally, so divide the total by the number of people:
$\frac{1500}{6} = 250.$
3. Check: $6 \times 250 = 1500$ . Good.

Each person raises $250$ dollars.

The answer is $\boxed{\textbf{(A)}\ 250}$ .

Why this works

Equal sharing means dividing the total by the number of people. The only hard part is the count: the words "you and five friends" include you. On early AMC problems the trap is usually in reading, not in arithmetic, so count carefully before you compute.

The trap

Dividing by 5 because the problem says five friends, which forgets you and gives 300, choice (B).

Concise solution

The group consists of you together with five friends, so six people share the work. Splitting $1500$ dollars into six equal parts gives
$\frac{1500}{6} = 250.$

The answer is $\boxed{\textbf{(A)}\ 250}$ .

Review in the AoPS books

Introduction to Algebra, Chapter 3: One-Variable Linear Equations (§3.3, §3.4)
Introduction to Algebra, Chapter 7: Proportion (§7.4)

Techniques

Set up the equation/formula and compute; no special trick needed