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2010 AMC 10B Problem 2

2010 AMC 10B Problem 2AMC 10 Step by Step

Name: Date: September 13, 2026

Ratios, Percents & Averages · difficulty 1 of 5 · about 1 min · position P1-10

Makayla attended two meetings during her $9$ -hour work day. The first meeting took $45$ minutes and the second meeting took twice as long. What percent of her work day was spent attending meetings?

A)
$15$
B)
$20$
C)
$25$
D)
$30$
E)
$35$

Answer

Key insight

Convert everything to minutes: 45 + 90 = 135 minutes of meetings out of 540, which is exactly one quarter.

Solution

The second meeting lasted $2 \cdot 45 = 90$ minutes, so the meetings took $45 + 90 = 135$ minutes in total.

Her work day is $9 \cdot 60 = 540$ minutes. The fraction spent in meetings is
$\frac{135}{540} = \frac{1}{4} = 25\%.$

The answer is $\boxed{\textbf{(C)}\ 25}$ .

Why this works

A percent is a ratio of a part to the whole, and a ratio only makes sense when both quantities are in the same unit. Pick the smaller unit (minutes) so that everything is an integer, then reduce the fraction.

Alternative approach

Work in hours: $135$ minutes is $2.25$ hours, and $2.25/9 = 0.25$ .

The trap

Comparing 135 minutes to 9 (hours) without converting units, or forgetting that the second meeting is 90 minutes, not 45.

Common mistakes

Comparing 135 minutes to 9 (hours) without converting units, or forgetting that the second meeting is 90 minutes, not 45.
Using only one meeting ( $45/540$ or $90/540$ ) and reporting about $8\%$ or about $17\%$ , then picking the nearest choice.

Techniques

Set up the equation/formula and compute; no special trick needed