What is a Story Problem with an Unknown?

S1-SA5-0276

Grade Level:

Class 5

All STEM domains, Finance, Economics, Data Science, AI, Physics, Chemistry

Definition

What is it?

A story problem with an unknown is a word problem that describes a real-life situation where one piece of information is missing. Your job is to use the given facts and mathematical operations to find that missing piece, which we call the 'unknown'.

Simple Example

Quick Example

Imagine your mother gave you some money to buy samosas. You bought 3 samosas for 10 rupees each, and you know you spent a total of 30 rupees. The unknown here is how much money your mother gave you initially if you had 5 rupees left. You need to figure out the starting amount.

Worked Example

Step-by-Step

PROBLEM: Priya has some colourful bangles. Her friend gave her 7 more bangles. Now Priya has a total of 15 bangles. How many bangles did Priya have to begin with?

Step 1: Understand the problem. We know Priya got 7 more bangles and ended up with 15. We need to find her starting number.
---Step 2: Identify the unknown. Let 'x' represent the number of bangles Priya had initially.
---Step 3: Formulate an equation. Starting bangles + added bangles = total bangles. So, x + 7 = 15.
---Step 4: Isolate the unknown. To find 'x', we need to subtract 7 from both sides of the equation.
---Step 5: Perform the calculation. x = 15 - 7.
---Step 6: Solve for x. x = 8.
---Step 7: Check your answer. If Priya started with 8 bangles and got 7 more, 8 + 7 = 15. This matches the total.
---Answer: Priya had 8 bangles to begin with.

Why It Matters

Understanding story problems with unknowns helps you solve puzzles in science, manage your pocket money, and even design apps! Engineers use this to calculate materials, and data scientists use it to find missing information in large datasets, helping companies make smart decisions.

Common Mistakes

MISTAKE: Adding numbers instead of subtracting (or vice-versa) when moving terms around. | CORRECTION: Always use the inverse operation. If a number is added to the unknown, subtract it from both sides. If it's multiplied, divide.

MISTAKE: Not clearly identifying what the 'unknown' actually represents before solving. | CORRECTION: Before starting, write down 'Let x = [what you need to find]'. This keeps your goal clear.

MISTAKE: Forgetting to check the answer by plugging it back into the original story. | CORRECTION: After finding your answer, read the original problem again and see if your answer makes sense in the context of the story.

Practice Questions

Try It Yourself

QUESTION: A auto-rickshaw driver completed a 25 km ride. He knows he had already driven some distance before this ride. If his total distance for the day became 40 km, how much did he drive before the 25 km ride? | ANSWER: 15 km

QUESTION: Your school library has a collection of storybooks. After buying 12 new storybooks, the library now has 75 storybooks. How many storybooks did the library have before the new purchase? | ANSWER: 63 storybooks

QUESTION: A street vendor sold some chai cups in the morning. In the afternoon, he sold 15 more cups. If he sold a total of 40 chai cups by the end of the day, and each cup costs 10 rupees, how many cups did he sell in the morning? | ANSWER: 25 cups

MCQ

Quick Quiz

Which of these is an 'unknown' in the problem: 'Rohan spent 50 rupees on snacks and had 20 rupees left. How much money did he have initially?'

50 rupees spent on snacks

20 rupees left

The initial amount of money Rohan had

The total number of snacks bought

The Correct Answer Is:

The question asks 'How much money did he have initially?', making the initial amount the missing piece of information we need to find, which is the unknown. The other options are known facts.

Real World Connection

In the Real World

When you use a ride-sharing app like Ola or Uber, the app's algorithm constantly solves problems with unknowns. For example, if a driver completes a trip and knows the distance covered and the total fare, the app might calculate the fuel cost (an unknown) per km to help the driver estimate earnings. Similarly, when managing your monthly mobile data, you might calculate how much data (unknown) you can use daily if you have a certain amount left for the remaining days.

Key Vocabulary

Key Terms

UNKNOWN: The missing piece of information you need to find in a problem | EQUATION: A mathematical statement showing that two expressions are equal | VARIABLE: A symbol (like 'x' or 'y') used to represent an unknown number | INVERSE OPERATION: An operation that undoes another (e.g., addition is the inverse of subtraction) | STORY PROBLEM: A word problem that describes a real-life situation

What's Next

What to Learn Next

Great job understanding unknowns! Next, you can explore 'Solving Equations with One Variable'. This will teach you more advanced techniques to find those tricky unknowns in slightly more complex story problems, building on what you've learned here.