AMC 8 · 2008 · #1

Grade 3 arithmetic

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

multi-digit-arithmeticmental-arithmetic identify-subproblems ↑ Prerequisites: multi-digit-arithmeticorder-of-operations

📏 Short solution 💡 2 insights

Problem

Susan brings

50</span> to the carnival. She spends <span class="mk-c">

12 on food and twice that on rides. How much money does she have left?

Pick an answer.

(A)

(B)

(C)

(D)

(E)

AMC 8 2008 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

How to solve

Strategy Identify Subproblems

Three things happen in order — food cost, rides cost, money left — and only the food cost is given directly. Tool #7 (Identify Subproblems) breaks the story into three single-step computations so each one stays simple. Tool #3 (Write an Equation) gives us the one short formula we need for each step (multiply for rides, add for total spent, subtract for what's left).

1STEP 1

Rides cost twice the $12 food, so doubling gives <span class="mk-a"><span class="hl-ask">$ 24.

rides = 2 × 12 = 24

2STEP 2

Add both purchases: $12 plus$ 24 gives $36 total spent.

total spent = 12 + 24 = 36

3STEP 3

Subtract the $36 spent from the$ 50 start to get $14 left.

left = 50 - 36 = 14 → (B)

Answer

Quick sanity pass:

12 on food plus

24 on rides is

36, and

36 +

14 =

50 matches the starting amount, so the answer balances. Also

14 is less than the

50 Susan started with and less than the

36 she spent, which is exactly what "left over" should look like. Choice (E)

50 would mean she spent nothing, and (D) $38 ignores the rides — neither fits the story.

💡Key takeaway

Three small steps in the right order — double, add, subtract — turn this AMC 8 problem into easy Grade 3 arithmetic.

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