Математика20 мин
Word Problems
A reliable 4-step framework for translating English into algebra without missing details.
01
The 4-step framework
- **Define variables** explicitly: ‘let = number of adults’.
- **Translate** every sentence into an equation or inequality.
- **Solve** the system — substitution, elimination, or single equation.
- **Check the units and the question**: did they ask for or ?
The last step catches half of all mistakes. Re-read the question after solving.
02
Common patterns
| Pattern | Setup |
|---|---|
| Distance / speed / time | , separate row per leg |
| Mixture / concentration | Total amount = sum of parts; concentration = amount / volume |
| Work rate | Rate = 1 / time; rates add when working together |
| Age | Express both ages in same year, build equation across years |
Speed/distance
A train leaves at 60 km/h. Two hours later, a car leaves on the same route at 90 km/h. When does the car catch up?
- Let = hours after the car leaves. Train has been going hours.
- Distances equal: .
- .
- Car catches up 4 h after it leaves, i.e. 6 h after the train.
Жауап: After 4 hours of driving