AMC 8 · 2000 · #1
Easy mode Grade 3Problem
Picture three people: Aunt Anna, Brianna, and Caitlin.
Aunt Anna is 42 years old. Brianna is half as old as Aunt Anna. Caitlin is 5 years younger than Brianna.
How old is Caitlin?
Pick an answer.
AMC 8 2000 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
Try it yourself first — the explanation is most useful after you’ve attempted it.
Toolkit + CCSS Solution
Understand
Restated: Aunt Anna is $42$. Brianna is half of Aunt Anna's age. Caitlin is $5$ years younger than Brianna. Find Caitlin's age.
Givens: Aunt Anna's age is $42$; Brianna's age is half of Aunt Anna's age; Caitlin's age is Brianna's age minus $5$; Answer choices: (A) $15$, (B) $16$, (C) $17$, (D) $21$, (E) $37$
Unknowns: Caitlin's age
Understand
Restated: Aunt Anna is $42$. Brianna is half of Aunt Anna's age. Caitlin is $5$ years younger than Brianna. Find Caitlin's age.
Givens: Aunt Anna's age is $42$; Brianna's age is half of Aunt Anna's age; Caitlin's age is Brianna's age minus $5$; Answer choices: (A) $15$, (B) $16$, (C) $17$, (D) $21$, (E) $37$
Plan
Primary tool: #7 Identify Subproblems
The question asks about Caitlin, but Caitlin's age is only described through Brianna, and Brianna's age is only described through Aunt Anna. Tool #7 (Identify Subproblems) says: when an unknown sits at the end of a chain of clues, split the work into two tiny subproblems — first find the middle person (Brianna), then use that to find the target (Caitlin). Each subproblem is one operation, so no algebra is needed.
Execute — Answer: B
3.OA.A.3 Step 1 - Subproblem 1: find Brianna's age.
- "Half as old as Aunt Anna" means divide Aunt Anna's $42$ by $2$.
💡 Dividing $42$ by $2$ is a Grade 3 multiplication/division-within-$100$ fact: $2 \times 21 = 42$.
2.OA.A.1 Step 2 - Subproblem 2: find Caitlin's age.
- "$5$ years younger than Brianna" means subtract $5$ from Brianna's $21$.
💡 $21 - 5 = 16$ is a Grade 2 within-$100$ subtraction fact.
3.OA.A.3 Subproblem 1: find Brianna's age. "Half as old as Aunt Anna" means divide Aunt A 2.OA.A.1 Subproblem 2: find Caitlin's age. "$5$ years younger than Brianna" means subtrac Review
Reasonableness: Check the chain forward: Aunt Anna $42$, half of that is $21$ (Brianna), five less is $16$ (Caitlin). Each relationship holds. The size also makes sense: Caitlin is younger than Brianna, who is younger than Aunt Anna, and $16 < 21 < 42$. Choice (E) $37$ would be Aunt Anna minus $5$ — a misread. Choice (D) $21$ is Brianna's age, not Caitlin's. The answer is (B) $16$.
Alternative: Tool #3 (Eliminate Possibilities): Brianna is $21$, and Caitlin is younger than Brianna, so Caitlin's age must be less than $21$. That immediately removes (D) $21$ and (E) $37$. From (A) $15$, (B) $16$, (C) $17$, only (B) $16$ makes the gap to Brianna exactly $5$.
CCSS standards used (min grade 3)
2.OA.A.1Use addition and subtraction within 100 to solve word problems (Subtracting $5$ from $21$ to find Caitlin's age is a Grade 2 word-problem subtraction within $100$.)3.OA.A.3Use multiplication and division within 100 to solve word problems (Halving $42$ to get Brianna's age is division within $100$ in a word-problem context.)
⭐ Two clues, two tiny steps: halve $42$, then subtract $5$. AMC 8 #1 only needs Grade 3 arithmetic when you split it into subproblems.
⭐ Two clues, two tiny steps: halve $42$, then subtract $5$. AMC 8 #1 only needs Grade 3 arithmetic when you split it into subproblems.
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