AMC 8 · 2015 · #1

Grade 5 geometry-2d

Archetype Arithmetic Expression Decomposition └ Sub-archetype Fraction / Expression Sum Evaluation

area-rectanglesunit-conversion dimensional-analysis ↑ Prerequisites: area-rectanglesmulti-digit-arithmetic

📏 Short solution 💡 2 insights

Problem

Onkon's room floor is a rectangle that measures 12 feet long and 9 feet wide. He wants to cover the whole floor with red carpet, but carpet is sold in square yards, not square feet. Using the fact that 3 feet = 1 yard, how many square yards of carpet does he need?

Pick an answer.

(A)

(B)

(C)

108

(D)

324

(E)

972

AMC 8 2015 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

How to solve

Strategy Analyze the Units

The trap of this problem is units: the dimensions come in feet but the answer must be in square yards. Tool #8 (Analyze the Units) keeps the bookkeeping honest — convert each side from feet to yards first (12 ft = 4 yd, 9 ft = 3 yd), then multiply to get area in square yards. Tool #1 (Draw a Diagram) helps younger solvers see why the answer is 12 and not 108: sketching the 4-yd by 3-yd rectangle and tiling it with 1-yd squares shows exactly 12 tiles, making the unit conversion concrete instead of abstract.

1STEP 1

Divide each side by 3: 12 ft becomes 4 yd and 9 ft becomes 3 yd.

12 ft ÷ 3 ft/yd = 4 yd, 9 ft ÷ 3 ft/yd = 3 yd

2STEP 2

Tile the 4 yd × 3 yd floor with 1-yd squares — 4 columns by 3 rows make 12 squares.

4 columns × 3 rows = 12 unit squares

3STEP 3

Both sides are in yards, so area = 4 × 3 = 12 square yards directly. → (A)

Area = 4 yd × 3 yd = 12 yd² → (A)

Answer

Cross-check by computing in square feet first: 12 × 9 = 108 square feet. Since 1 square yard = 3 ft × 3 ft = 9 square feet, the floor is 108 ÷ 9 = 12 square yards. Same answer, (A). The trap answer 108 appears as choice (C), which is the result if a solver forgets to convert. The other choices (36, 324, 972) come from dividing or multiplying by 3 instead of 9 — clear sign that the units must be tracked carefully.

💡Key takeaway

This AMC 8 problem only needs Grade 5 unit conversion plus the Grade 4 rectangle area formula you already know!

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