AMC 10 · 2010 · #2

Grade 6 rate-ratio

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

percentageunit-conversionfraction-arithmetic identify-subproblems ↑ Prerequisites: percentageunit-conversion

📏 Medium solution 💡 2 insights

Problem

During a 9-hour work day, Makarla attended two meetings: the first lasted 45 minutes and the second lasted twice as long. Find what percent of her work day she spent in meetings.

Pick an answer.

(A)

(B)

(C)

(D)

(E)

AMC 10 2010 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.

How to solve

Strategy Identify Subproblems

The question stacks a few small tasks: find the second meeting's length, add the two meetings, express the day in the same unit, then turn the ratio into a percent. Tool #7 (Identify Subproblems) keeps each step clean. Tool #8 (Analyze the Units) is the guardrail: the day is in hours and the meetings in minutes, so the one real trap is comparing them before matching units. Convert the day to minutes and the percent falls out.

1STEP 1

Double the first meeting

The second meeting is twice the first, so it ran 2 × 45 = 90 minutes.

2 × 45=90 minutes

2STEP 2

Add the two meetings

Add the two meetings: 45 + 90 = 135 minutes of meeting time.

45+90=135 minutes

3STEP 3

Convert the day to minutes

Match the units: 1 hour is 60 minutes, so the day is 9 × 60 = 540 minutes.

9 × 60=540 minutes

4STEP 4

Turn the ratio into a percent

Part over whole: $\frac{135}{540}=\frac{1}{4}$ , which is 25%, so the answer is (C).

135/540=1/4=25% → (C)

Answer

The meetings run 135 minutes out of a 540-minute day — a bit more than two hours out of nine, which is roughly a quarter of the day. 25% matches that eyeball estimate, and it lands right in the middle of the choices, so it is the sensible size. Answers like 15% would be far too little for over two hours of meetings.

💡Key takeaway

Before you compare two amounts, make sure they are in the same unit — then the percent is just part over whole.

Double the first meeting
Add the two meetings
Convert the day to minutes
Turn the ratio into a percent

Double the first meeting

Add the two meetings

Convert the day to minutes

Turn the ratio into a percent

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