Makayla attended two meetings during her -hour work day. The first meeting took minutes and the second meeting took twice as long. What percent of her work day was spent attending meetings?
- A)
- B)
- C)
- D)
- E)
Answer
C
Key insight
Put everything in minutes. The meetings take 45 + 90 = 135 minutes, and the work day is 9 times 60 = 540 minutes, exactly four times as long.
Solution
A percent compares a part with the whole, and both must be in the same unit. Minutes keep every number whole, so use minutes.
1. The second meeting took twice as long as the first: minutes.
2. Both meetings together: minutes.
3. The work day: hours is minutes.
4. The fraction of the day in meetings is
Since , this is , which is .
The answer is .
Why this works
A percent is just a fraction of the whole, written out of . Before dividing, make sure the part and the whole use the same unit; choosing the smaller unit (minutes) avoids decimals.
Alternative approach
Work in hours instead. minutes is hours and minutes, or hours. Then .
The trap
Forgetting that the second meeting lasts twice as long (90 minutes, not 45), or comparing minutes with hours without converting.
Concise solution
The second meeting lasted minutes, so the meetings took minutes in total.
Her work day is minutes. The fraction spent in meetings is
The answer is .
Review in the AoPS books
- Introduction to Algebra, Chapter 6: Ratios and Percents
- Introduction to Algebra, Chapter 7: Proportion (§7.1, §7.2, §7.3)
- Prealgebra, Chapter 13: Data and Statistics (§13.1)
Techniques
Set up the equation/formula and compute; no special trick needed