Water and wastewater · Worked step by step

What percent of capacity is 400 GPM out of 500?

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The problem

A pump is rated for 500 GPM but is running at 400 GPM. What percent of its capacity is it running at?

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2 steps

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The written version, step by step

  1. 1

    Set up part over whole

    part = 400 GPM • whole = 500 GPM

    • The pump is doing 400 GPM. That is the part.
    • It could do 500 GPM at full capacity. That is the whole.
    • Percent compares the part to the whole.

    Quick trick: The 'whole' is whatever full or maximum you are measuring against, here the 500 rating.

  2. 2

    Divide, then make it a percent

    400 ÷ 500 = 0.8 • 0.8 × 100 = 80%

    • Divide the part by the whole: 400 ÷ 500 = 0.8.
    • Turn the decimal into a percent by multiplying by 100 (move the dot two places).
    • 0.8 becomes 80%. So the pump is at 80% of capacity. That is answer b.

    Quick trick: 400 ÷ 500: drop a zero from each to get 40 ÷ 50 = 0.8. Then 0.8 is 80%.

Remember this for good

Percent = part ÷ whole × 100. The 'whole' is the full capacity you are comparing against.

Percent is always the part over the whole. Here 400 is the part, 500 is the whole. 400 out of 500 is 80 out of 100, which is 80%.

Solve it fast next time

  • Percent = part ÷ whole × 100.
  • The whole is the full capacity (500), always the bigger, reference number.
  • If the part is less than the whole, the percent is under 100. That is a quick sanity check.

The answer: 80% of capacity.

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