What is Using Algebra to Solve a Word Problem?

S1-SA5-0624

Grade Level:

Class 5

Maths, Computing, AI, Physics, Economics

Definition

What is it?

Using algebra to solve a word problem means translating a story problem into a mathematical equation using letters (like 'x' or 'y') to represent unknown numbers. Once you have the equation, you can solve it to find the value of the unknown number and answer the original problem.

Simple Example

Quick Example

Imagine your friend has some cricket cards, and you give him 5 more. Now he has 12 cards. How many cards did he have before? We can say he had 'x' cards. So, x + 5 = 12. Solving this gives us x = 7.

Worked Example

Step-by-Step

PROBLEM: Reema bought a few samosas. Her brother ate 2 of them. Now Reema has 5 samosas left. How many samosas did Reema buy?

Step 1: Understand the problem. We need to find the original number of samosas Reema bought.
---Step 2: Assign a variable. Let 's' be the number of samosas Reema bought initially.
---Step 3: Write the equation based on the story. She bought 's' samosas, her brother ate 2 (so we subtract 2), and 5 are left. So, s - 2 = 5.
---Step 4: Solve the equation. To get 's' alone, we add 2 to both sides of the equation: s - 2 + 2 = 5 + 2.
---Step 5: Simplify. This gives us s = 7.
---Step 6: Check your answer. If Reema bought 7 samosas and her brother ate 2, she would have 7 - 2 = 5 samosas left. This matches the problem.

ANSWER: Reema bought 7 samosas.

Why It Matters

This skill helps you think logically and solve problems in many fields. Engineers use it to design bridges, computer scientists use it to write code, and economists use it to understand market trends. It's a foundational skill for careers in technology, science, and even business planning.

Common Mistakes

MISTAKE: Not reading the problem carefully and using the wrong operation (e.g., adding instead of subtracting) | CORRECTION: Read the problem at least twice. Underline keywords like 'total', 'left', 'more than', 'less than' to identify the correct mathematical operation.

MISTAKE: Forgetting to define what the variable represents | CORRECTION: Always start by saying, 'Let x be...' or 'Let y represent...' This makes your solution clear and helps avoid confusion.

MISTAKE: Not checking the answer to see if it makes sense in the original word problem | CORRECTION: After solving, plug your answer back into the original problem's story to ensure it fits logically and mathematically.

Practice Questions

Try It Yourself

QUESTION: A auto-rickshaw driver completed 3 trips and earned Rs 150. If he earned the same amount for each trip, how much did he earn per trip? | ANSWER: Rs 50

QUESTION: My mobile data pack gives me 10 GB per month. After using some data, I have 3 GB left. How much data did I use? | ANSWER: 7 GB

QUESTION: Priya had some money. She spent Rs 75 on a book and Rs 25 on a pen. She now has Rs 100 left. How much money did Priya have initially? | ANSWER: Rs 200

MCQ

Quick Quiz

Which equation correctly represents the problem: 'Rohan has 'x' marbles. If he doubles his marbles and adds 5, he will have 25 marbles.'?

x + 5 = 25

2x + 5 = 25

x + 2 + 5 = 25

2x - 5 = 25

The Correct Answer Is:

Doubling 'x' marbles means 2 times x, or 2x. 'Adds 5' means + 5. 'Will have 25' means = 25. So, the correct equation is 2x + 5 = 25.

Real World Connection

In the Real World

When you use apps like Swiggy or Zomato, the delivery system uses algebra to calculate the best route, time, and cost based on distance and traffic. Even when ISRO scientists launch rockets, they use complex algebraic equations to figure out fuel, speed, and trajectory to reach space successfully.

Key Vocabulary

Key Terms

VARIABLE: A letter (like x or y) that stands for an unknown number | EQUATION: A mathematical statement that shows two expressions are equal, usually with an '=' sign | WORD PROBLEM: A math problem presented in a story or sentence format | SOLVE: To find the value of the unknown variable in an equation

What's Next

What to Learn Next

Next, you can learn about solving equations with variables on both sides, which is a step up from these basic problems. This will help you tackle even more complex real-life situations and prepare you for higher-level math concepts.