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Difficulty: MediumPercentage Calculations

A logistics convoy is transporting supplies to a remote base. On the first day of the trip, they complete 30%30\% of the total distance. On the second day, they complete 40%40\% of the remaining distance. If they still have 210210 miles left to travel, what is the total distance of the trip in miles?

  1. A
    350
  2. 500Answer
  3. C
    700
  4. D
    750

Answer

The total distance of the trip is 500 miles.
The correct answer accurately accounts for the successive percentages by applying the second day's percentage to the remaining distance. After traveling 30% of the trip, 70% remains. Leaving 40% of this remaining 70% completed means 60% of the 70% is left uncompleted, which equals 42% of the total distance. Setting 42% equal to the 210 remaining miles gives a total distance of 500 miles.

Step-by-Step Solution

1
Determine the percentage of the trip remaining after the first day.
100%−30%=70%100\% - 30\% = 70\%
The second day's travel is based on the remaining distance, not the total distance.
2
Calculate the percentage of the remaining distance that is left after the second day.
100%−40%=60%100\% - 40\% = 60\%
Since they completed 40% of the remaining distance, 60% of that remaining distance is still uncompleted.
3
Calculate the percentage of the total distance that the final remaining 210 miles represents.
0.70×0.60=0.420.70 \times 0.60 = 0.42, which is 42%42\% of the total distance.
Successive percentages are applied by multiplying the decimal forms of the remaining portions.
4
Set up an equation to solve for the total distance, D.
0.42D=210  ⟹  D=210÷0.42=5000.42D = 210 \implies D = 210 \div 0.42 = 500
Dividing the remaining miles by the remaining percentage of the total trip yields the original total distance.

Key Concept

Calculating successive percentage changes by adjusting the base for each subsequent calculation.
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Topics

Percentage Calculations

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