AMC 10 · 2003 · #2
Grade 5 arithmeticPick an answer.
The 2366 total looks scary until you split the job into small parts. Tool #7 (Identify Subproblems) breaks it into three easy steps: first find the T-shirt price, then find what ONE member spends, then see how many of those equal-size member bills fit inside2366. Tool #8 (Analyze the Units) keeps the dollars straight and stops the classic trap of buying only one pair of socks and one shirt instead of two of each. Once one member's bill is a single number, the last step is just a division.
Price one T-shirt
A shirt is five more than socks, so it costs 9.
"5 to what the socks cost.
2.OA.A.1Identify SubproblemsAdd up one member's bill
Home and away means two of each, so one member spends 26.
Home plus away means everything is bought twice, so one member's cost is two socks and two shirts.
3.OA.D.8Identify SubproblemsCount how many members fit in $2366
Dividing the total by that bill gives exactly 91 members, choice (B).
If every member's bill is the same size, the count is just the total split into equal pieces.
Since every member's bill is the same size, the number of members is the total split into equal pieces.
▸ Why?
Many members each paying the same amount is a count of equal groups, which is what multiplying records.
▸ Why?
Dividing undoes multiplying, so the total shared by one member's bill hands back how many members there are.
Find what one person spends first, then divide the grand total by it to see how many people there were.
- Price one T-shirt
- Add up one member's bill
- Count how many members fit in $2366