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Simple and compound rules of three
This is a mathematical model used to solve proportion problems, the problems can involve direct or indirect proportional quantities. it can be simple or compound.
Simple Rule of Three
Simple rule of three involves only two direct or indirect proportional quantities.
- if 2 products cost $10, how much 5 products will cost?
- \[2/10 = 5/x ⇒ 2x = 10.5 ⇒ 2x = 50 ⇒ x = 25\]
Compound Rule of Three
Involves more than two quantities, could be direct or indirect proportional quantities.
- If 6 workers build a wall in 10 days working 8 hours per day,
how many workers are needed to build the same wall in 5 days, working 6 hours per day?
- Identify the quantities:
- Workers (W)
- Days (D)
- Hours per day (H)
- Set up the table:
- Identify the quantities:
| Workers (W) | Days (D) | Hours per Day (H) |
|---|---|---|
| 6 | 10 | 8 |
| x | 5 | 6 |
- The relationships:
- Days and Workers: Fewer days require more workers (inverse proportion).
- Hours and Workers: Fewer hours per day require more workers (inverse proportion).
- \[6.10.8 = x.5.6 ⇒ 6.10.8 = x.30 ⇒ 480 = x.30 ⇒ x = 16\]
References
- Carman, Robert A., and Hal M. Saunders. Mathematics for the Trades.
- Bluman, Allan G. Pre-Algebra Demystified.
- Purplemath: Proportions