A story becomes a pair
A story with two facts hides two equations. In the lab, drag the total in fact two. Its line moves. The two lines cross at the answer.
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- The story: two samosas with three chai cost ₹65, one of each costs ₹25.
- Name the letters: x = one samosa, y = one chai.
- Fact one becomes
2x + 3y = 65. - Fact two becomes
x + y = 25.
The rule
Name the letters first. Write one equation for each fact. Then solve. Each equation is a line. The lines cross at the answer.
Example
Let x be the price of one samosa, in rupees. Let y be the price of one chai, in rupees. Now each letter stands for one price, with its unit.
The two facts give 2x + 3y = 65 and x + y = 25. The second equation gives x = 25 − y. Use that in the first: 2(25 − y) + 3y = 65. Open the bracket: 50 − 2y + 3y = 65. So 50 + y = 65 and y = 15. Then x = 25 − 15 = 10.
Check both. 2×10 + 3×15 = 20 + 45 = 65. 10 + 15 = 25. A samosa costs ₹10 and a chai costs ₹15.
| Move | What it does |
|---|---|
| Name the letters | Gives every number an owner and a unit. |
| Write fact one | Turns a sentence into an equation. |
| Write fact two | Turns the second sentence into one. |
| Solve the pair | Finds the two numbers. |
| Check both, then answer | Put the numbers back. Write a sentence. |
Watch out!
Read which side is bigger. Say tank 1 holds x litres and tank 2 holds y litres. If tank 1 holds 3 litres more, write x = y + 3. Do not write y = x + 3.