2004 AMC 10A Problem 1

P1-10~1 minPrint

Linear Equations & Word Problems Set up the equation/formula and compute; no special trick needed

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?

Show solution without answering

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.

Concise solution

A shorter write-up, the way contest solutions are usually written. It may take a different route from the solution above.

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)