A music concert is 3 hours long. During the concert there is one 27-minute intermission. Approximately what percentage of the concert is the intermission?
A 5%
B 10%
C 12%
D 15%
The correct answer and explanation is :
To solve this problem, we first need to calculate what percentage 27 minutes is of the total concert time.
Step 1: Convert the concert time into minutes
3 hours = 3 × 60 = 180 minutes
Step 2: Calculate the percentage of the intermission
We use the formula:
$$
\text{Percentage} = \left( \frac{\text{Intermission Time}}{\text{Total Concert Time}} \right) \times 100
$$
$$
\text{Percentage} = \left( \frac{27}{180} \right) \times 100 \approx 15\%
$$
Correct Answer: D. 15%
Explanation (300 words):
To find out what percentage of the concert is taken up by the 27-minute intermission, we must first understand that percentages are a way of expressing one quantity as a fraction of another, out of 100. In this case, we are comparing the intermission time (27 minutes) to the total duration of the concert (3 hours), and we want to know what fraction of the total time the intermission represents.
Since the concert duration is given in hours and the intermission is in minutes, the first step is to convert the concert duration into minutes. There are 60 minutes in an hour, so 3 hours is equivalent to 3 × 60 = 180 minutes. Now both the concert duration and the intermission are in the same units, which makes comparison straightforward.
Next, we use a simple percentage formula:
$$
\left( \frac{\text{part}}{\text{whole}} \right) \times 100
$$
Here, the “part” is the intermission (27 minutes) and the “whole” is the full concert (180 minutes). Substituting these into the formula gives:
$$
\left( \frac{27}{180} \right) \times 100 = 15\%
$$
This calculation shows that the intermission takes up exactly 15% of the total concert time. Among the answer choices provided—5%, 10%, 12%, and 15%—the correct answer is clearly D. 15%. This kind of percentage problem is common in time management and scheduling scenarios, making it a useful skill in both academic and real-world settings.