Day 6: Translating the World (Word Problems) | Secondary Stage (Grades 9 & 10) | Apex Institute of Maths and Sciences

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Day 6: Translating the World (Word Problems) | Secondary Stage (Grades 9 & 10) | Apex Institute of Maths and Sciences

Day 6: Translating the World (Word Problems) 🌍🧮

Secondary Stage (Grades 9 & 10) | Apex Institute of Maths and Sciences

🎯 1. Concept: Math is a Language

Welcome to Day 6! You know how to use Substitution and you know how to use Elimination. But in the real world, problems don’t come neatly packaged as “Solve for x and y”. They come as paragraphs of text.

Today, you become a translator. Your job is to read English sentences and translate them into Algebraic Equations. Once the equations are set up, you can use the tools you already know to solve them!

💡 2. The Dictionary of Algebra

To translate successfully, look for the keyword triggers:

  • Sum / Total: Means Addition (+)
  • Difference / More than: Means Subtraction (-)
  • Times / Product: Means Multiplication (×)
  • Is / Was / Will be: Means Equals (=)

Example: “The sum of two numbers is 15. The first number is 3 more than the second.”
Translation: Let the numbers be x and y.
Equation 1: x + y = 15
Equation 2: x = y + 3

🌍 3. Math in Our Daily Life

Word problems are just real-life mysteries waiting to be solved!

Scenario 1 (The Bank Teller): A bank teller has a stack of ₹100 notes and ₹500 notes. There are 30 notes in total, and the total cash value is ₹7,000. How many of each note are there? The teller translates this to: x + y = 30 and 100x + 500y = 7000 to figure it out fast!

Scenario 2 (Travel Speeds): You are driving against the wind. It takes 4 hours to drive 200 km. On the way back, with the wind pushing you, it takes 2 hours. What is the speed of your car, and what is the speed of the wind? Engineers use systems to calculate this exactly.

📝 4. Analytical Tasks

Open your math journal and complete these translation tasks (do not solve them, just translate them):

  • Task A: Translate: “Three times a number x, minus another number y, is exactly 12.”
  • Task B: Translate: “A movie theater sold adult tickets (a) for ₹200 and child tickets (c) for ₹100. They made ₹5000 in total.”

✅ 5. Day 6 Application Test

Can you translate English into Algebra? This quiz gets progressively harder, ending with full IIT-JEE foundation puzzles. Select your answers below and click submit.

Easy
1. How do you translate the sentence “The sum of two numbers, x and y, is 20” into an equation?
Solution: The word “sum” always means addition. Therefore, x + y = 20.
Easy
2. How do you translate the sentence “The difference between x and y is 5”?
Solution: The word “difference” means the result of subtraction. Therefore, x – y = 5.
Easy
3. How do you translate “Three times a number x is equal to y”?
Solution: “Three times” means multiply by 3. Therefore, 3 * x = y, or simply 3x = y.
Easy
4. In a word problem, what mathematical symbol does the word “is” usually represent?
Solution: “Is” represents a state of equality. It almost always means the equals sign (=).
Medium
5. You buy 4 shirts (s) and 2 pants (p) for ₹2000. Which equation correctly translates this?
Solution: The cost of 4 shirts is 4s, and 2 pants is 2p. The total is 2000. So, 4s + 2p = 2000.
Medium
6. A farmer has chickens (c) and cows (w). The total number of animals (heads) is 40. Which equation represents this?
Solution: We are just counting heads, meaning 1 per animal. The number of chickens plus cows equals 40. So, c + w = 40.
Medium
7. Using the farmer from the previous question: chickens have 2 legs, cows have 4 legs. The total number of legs is 100. Which equation represents the LEGS?
Solution: Multiply the number of chickens by 2, and the cows by 4. Therefore, 2c + 4w = 100.
Medium
8. Solve this simple translated system: The sum of two numbers is 12 (x + y = 12). Their difference is 2 (x – y = 2). What is the larger number (x)?
Solution: Use elimination! Add the equations: (x + x) = 2x. The y’s cancel. (12 + 2) = 14. 2x = 14, so x = 7.
Hard
9. 🧠 Puzzle: A stationery shop sells pens for ₹10 and pencils for ₹5. You buy a total of 15 items, and your total bill is ₹100. How many pens did you buy?
Solution: Eq 1 (Items): p + c = 15. Eq 2 (Cost): 10p + 5c = 100. Multiply Eq 1 by 5: 5p + 5c = 75. Subtract from Eq 2: (10p – 5p) = 5p. The c’s cancel. 100 – 75 = 25. 5p = 25, so p = 5. You bought 5 pens!
Hard
10. 🧠 Puzzle: Three cups of coffee and two donuts cost ₹180. If you subtract the donuts, two cups of coffee and two donuts cost ₹140. What is the price of ONE cup of coffee?
Solution: Eq 1: 3c + 2d = 180. Eq 2: 2c + 2d = 140. Use elimination by subtraction! 3c – 2c = 1c. The 2d’s cancel out. 180 – 140 = 40. One coffee is ₹40!
⚠️ Please answer all 10 questions before submitting!
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