AMC 8 · 2002 · #9

Grade 4 arithmetic

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

graph-readingmulti-digit-arithmeticunit-conversion identify-subproblems ↑ Prerequisites: multi-digit-arithmetic

📏 Short solution 💡 2 insights 📊 Diagram

Problem

Juan's stamps are grouped by country (Brazil, France, Peru, Spain) and by decade (50s, 60s, 70s, 80s). Brazilian and French stamps cost 6 cents each, Peruvian stamps 4 cents each, and Spanish stamps 5 cents each. Brazil and Peru are the South American countries. Find the total cost, in dollars and cents, of his South American stamps that were issued before the 70s.

Pick an answer.

(A)

$0.40

(B)

$1.06

(C)

$1.80

(D)

$2.38

(E)

$2.64

AMC 8 2002 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

How to solve

Strategy Break into Subproblems

The table has 16 cells but the question only cares about a small rectangle of them: two rows (Brazil, Peru) by two columns (50s, 60s). Tool #2 (Make an Organized List) pulls out exactly those four cells with the right per-stamp price attached. Tool #7 (Break into Subproblems) then handles them one country at a time: total Brazil stamps from those decades times 6 cents, total Peru stamps times 4 cents, then add. Splitting by country is the right cut because price changes with country, not with decade.

1STEP 1

"South American" keeps Brazil and Peru; "before the 70s" keeps the 50s and 60s — so from the table, Brazil 4 and 7, Peru 6 and 4.

Brazil: 4 (50s), 7 (60s) Peru: 6 (50s), 4 (60s)

2STEP 2

Add Brazil's two decade counts and multiply by its 6-cent price to get 66 cents.

Brazil cost = (4 + 7) × 6 = 11 × 6 = 66 cents

3STEP 3

Do the same for Peru at its 4-cent price to get 40 cents.

Peru cost = (6 + 4) × 4 = 10 × 4 = 40 cents

4STEP 4

Add the two subtotals — 106 cents — and convert to dollars and cents by dividing by 100.

66 + 40 = 106 cents = $1.06 → (B)

Answer

$1.06

Check the filter held: France (6 cents each) and Spain (5 cents each) were dropped (not South American), and the 70s and 80s columns were dropped (not before the 70s). Eleven Brazil stamps at 6 cents each is

0.66; ten Peru stamps at 4 cents each is

0.40; together

1.06, matching (B). The trap (A)

0.40 is Peru only, (C)

1.80 includes the 70s, and (E)

2.64 includes all four decades — easy to spot once you know the right filter.

💡Key takeaway

Big tables hide small questions. Use the wording to throw out everything you don't need (France, Spain, the 70s and 80s), then handle each country at its own price. Two short multiplications and an add — 11 × 6 + 10 × 4 = 106 cents = $1.06 — finish the problem.

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