AMC 8 · 2020 · #3

Grade 4 arithmeticgeometry-2d

Archetype Arithmetic Expression Decomposition └ Sub-archetype Weighted Group Aggregation

area-rectanglesratemulti-digit-arithmetic identify-subproblemsdimensional-analysis ↑ Prerequisites: area-rectanglesmulti-digit-arithmetic

📏 Short solution 💡 2 insights

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Problem

Carrie has a rectangular strawberry garden measuring 6 feet by 8 feet. She fits 4 plants in every square foot, and each plant gives an average of 10 strawberries. How many strawberries total can she expect to harvest from the whole garden?

Pick an answer.

(A)

560

(B)

960

(C)

1120

(D)

1920

(E)

3840

AMC 8 2020 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

How to solve

Strategy Identify Subproblems

The question "how many strawberries" hides three smaller questions stacked on top of each other: (1) how much area is the garden? (2) how many plants fit in that area? (3) how many strawberries do those plants give? Tool #7 (Identify Subproblems) makes that ladder explicit so we never multiply the wrong pair of numbers. Tool #8 (Analyze the Units) is the safety check at each rung — square feet × plants/sq ft cancels to plants, and plants × strawberries/plant cancels to strawberries — so the units guarantee we have the right quantity at every step.

1STEP 1

Subproblem 1: the garden is a rectangle, so its area is 6 × 8 = 48 sq ft.

6 ft × 8 ft = 48 sq ft

2STEP 2

Subproblem 2: multiply the area by 4 plants per square foot to get 192 plants.

48 sq ft × 4 plants/(sq ft) = 192 plants

3STEP 3

Subproblem 3: multiply 192 plants by 10 strawberries each to get 1920 strawberries.

192 plants × 10 strawberries/plant = 1920 strawberries → (D)

Answer

1920

The whole calculation is one long multiplication, 6 × 8 × 4 × 10 = 1920. We can re-bracket it as (6 × 8) × (4 × 10) = 48 × 40 = 1920 to double-check — same answer. The magnitude also makes sense: a small backyard plot (48 sq ft) packed with 192 plants and a generous 10 berries each should land in the low thousands of berries, exactly where 1920 sits. Choices like 560 or 3840 would mean we forgot a factor or doubled one.

💡Key takeaway

This AMC 8 problem only needs Grade 4 multi-step multiplication word problems you already know!

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