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Difficulty: MediumFractions, Decimals, and Percentages

A solar power plant generated a total of 480 megawatt-hours (MWh)480\text{ megawatt-hours (MWh)} of energy in one month. Of this total, 25\frac{2}{5} was stored in battery banks, 0.350.35 was supplied directly to an industrial facility, and the remaining portion was delivered to residential homes. How many megawatt-hours of energy were delivered to residential homes?

  1. A
    168 MWh
  2. B
    192 MWh
  3. 120 MWhAnswer
  4. D
    216 MWh
  5. E
    360 MWh

Answer

120 MWh
Converting 25\frac{2}{5} to 0.400.40 allows us to sum the battery and industrial portions (0.40+0.35=0.750.40 + 0.35 = 0.75). The remaining residential portion is 1−0.75=0.251 - 0.75 = 0.25, or 25%25\%. Taking 25%25\% of 480 MWh480\text{ MWh} gives 120 MWh120\text{ MWh}.

Step-by-Step Solution

1
Convert the fraction to a decimal
25=0.40\frac{2}{5} = 0.40
Converting all given values to a common format (decimals) simplifies addition.
2
Sum the non-residential portions of energy
0.40 + 0.35 = 0.75
Combining the battery storage fraction and industrial supply fraction determines the total non-residential portion.
3
Find the remaining fraction for residential homes
1.00 - 0.75 = 0.25
Subtracting the combined non-residential portion from the whole (1.00) gives the residential fraction.
4
Calculate the megawatt-hours delivered to residential homes
0.25 \times 480 = 120\text{ MWh}
Multiplying the residential fraction by the total energy generated gives the target quantity.

Key Concept

Combining fractions and decimals to determine a remaining percentage of a whole quantity
Estimated Time:1m 0s
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Topics

Fractions, Decimals, and Percentages

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