Wastewater · Worked step by step
What percent of the BOD was removed?
If math has never been your thing, you are in the right place. Try it on paper first, then we write it out with you, one small step at a time, and explain every step in plain words so you never lose the thread.
The problem
Wastewater comes in with a BOD of 200 mg/L and leaves with a BOD of 20 mg/L. What percent of the BOD was removed?
Grab a pen and paper first
Give it a real try on paper before you watch. If you get stuck, take a hint. If you go blank, that is fine, press play and we will walk it through together.
Watch it solved, with you
Every step is written out slowly and explained in plain words, so you always know what just happened. Nobody skips ahead and leaves you behind.
Press play and I’ll write it out with you, one small step at a time.
Every step gets a plain-words explanation here, so you always know exactly what just happened and why.
The written version, step by step
- 1
Find how much was removed
removed = 200 - 20 • removed = 180 mg/L
- First, how much BOD did we take out?
- It came in at 200 and left at 20. The difference is what got removed.
- 200 - 20 = 180 mg/L removed.
Quick trick: "Removed" always means in minus out. Do the subtraction first.
- 2
Divide by what you started with
percent = 180 ÷ 200
- Percent removed compares what we took out to what we started with.
- We started with 200, so we divide the 180 by 200.
- Always divide by the starting (in) number, not the leftover.
Quick trick: 180 ÷ 200 is the same as 0.9. Dividing by 200? Halve the top and divide by 100.
- 3
Turn it into a percent
percent = 0.9 × 100 • percent = 90%
- 180 ÷ 200 = 0.9.
- To make a decimal a percent, multiply by 100 (just move the dot two spots).
- 0.9 becomes 90%. So 90% of the BOD was removed. That is answer c.
Quick trick: A good plant removes most of the BOD, so a high percent like 90% should feel right.
Remember this for good
Percent removed = (what you took out ÷ what you started with) × 100. It always compares the change to the starting amount.
Think of a jar with 200 marbles. You take out 180 and leave 20. You removed 180 out of the original 200, and 180 out of 200 is 90 out of 100, which is 90%.
Solve it fast next time
- Two steps: first subtract to find how much was removed, then divide by what you STARTED with.
- Always divide by the IN number (the start), never the out number.
- Multiply by 100 at the end to make it a percent.
The answer: 90% removed.