AMC 8 · 2005 · #2

Grade 6 arithmetic

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

percentagemulti-digit-arithmeticfraction-multiplication identify-subproblems ↑ Prerequisites: multi-digit-arithmeticpercentage

📏 Short solution 💡 2 insights

Problem

Karl bought 5 folders at $2.50 each. The next day, the store had a 20%-off sale. How much money could Karl have saved by waiting one day?

Pick an answer.

(A)

$\textdollar 1.00$

(B)

$\textdollar 2.00$

(C)

$\textdollar 2.50$

(D)

$\textdollar 2.75$

(E)

$\textdollar 5.00$

AMC 8 2005 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

How to solve

Strategy Identify Subproblems

The question splits cleanly into two small jobs (Tool #7, Identify Subproblems): first find the original total cost of all 5 folders, then take 20% of that total to get the savings. Tool #16 (Change Focus) gives a faster shortcut: since 20% = $\frac{1}{5}$ , taking 20% of "5 folders" is the same as the cost of 1 folder. Both routes land on the same answer; the subproblem route confirms it with a direct calculation.

1STEP 1

First subproblem: multiply the 5 folders by the price of each to get the original total, $12.50.

Total cost = 5 ×

2.50 =

12.50

2STEP 2

Second subproblem: the savings is 20% of that total — one fifth of $12.50, which is <span class="mk-a"><span class="hl-ask">$ 2.50 (C).

Savings = 20% ×

12.50 =

\frac{1}{5}

×

12.50 = $2.50 → (C)

Answer

textdollar 2.50

Quick sanity check: 20% of

10 would be

2, so 20% of a number a bit bigger than

10 should be a bit bigger than

2. The answer

2.50 fits, and it sits between (B)

2.00 and (D)

2.75 in the right place. The two extreme choices fail: (A)

1.00 would be only 8% of

12.50, and (E)

5.00 would be 40% — neither matches the 20% discount.

💡Key takeaway

20% off five folders is the same as one folder free — that shortcut turns this AMC 8 problem into a Grade 6 percent-of-a-quantity exercise.

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