Compound Rule of Three
Solve problems involving multiple related quantities. Add as many variables as you need and mark each one as directly or inversely proportional.
Define what you want to calculate and add the variables that affect the result. Mark each one as directly or inversely proportional.
| Variable | Situation 1 | Situation 2 | Relation | |
|---|---|---|---|---|
| unknown | ||||
💡 How do I know if it's direct or inverse?
Directly proportional: when one increases, the other increases too. Ex.: more hours worked → more output.
Inversely proportional: when one increases, the other decreases. Ex.: more workers → less time to finish the job.
What is Compound Rule of Three?
Compound rule of three solves problems with three or more proportional quantities. Example: if 3 workers build 2 houses in 60 days, how many days will 5 workers take to build 4 houses? The calculator handles direct and inverse proportions automatically.
How to use
- Pick how many quantities your problem has.
- For each, mark if it's directly or inversely proportional.
- Fill in the known values.
- The unknown (X) is computed automatically.
Classic example
Problem:
"If 5 workers, working 8 hours a day, finish a job in 12 days, how many days would 8 workers working 6 hours a day take?"
- • Result (days): 12 → ?
- • Workers: 5 → 8 — inverse relation (more workers, fewer days)
- • Hours/day: 8 → 6 — inverse relation (fewer hours, more days)
- • Answer: 12 × (5/8) × (8/6) = 10 days
Frequently asked questions
What is the compound rule of three?
It is the generalization of the simple rule of three for more than one quantity. Example: if 5 workers take 10 days to do a job, how many days would 8 workers take? Two quantities (workers and days) are inversely proportional.
How do I know if a relation is direct or inverse?
Ask: "if this variable increases, does the result also increase?" If yes, DIRECT. If it decreases, INVERSE. Ex.: more workers → fewer days (inverse). More hours → more output (direct).
Can I use it with 3 or more variables?
Yes. Add as many variables as you need with the "+ Add variable" button. Each one with its own relation (direct or inverse).
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