What is Having Two Unknowns?

S1-SA5-1009

Grade Level:

Class 5

Maths, Computing, AI, Physics, Logic

Definition

What is it?

Having two unknowns means you have two different things whose values you don't know in a problem. These unknowns are usually represented by different letters, like 'x' and 'y'. To find the values of both unknowns, you typically need at least two separate pieces of information or equations.

Simple Example

Quick Example

Imagine you bought some samosas and some jalebis. You know the total cost, but you don't know how much one samosa costs and how much one jalebi costs. Here, the cost of a samosa and the cost of a jalebi are your two unknowns.

Worked Example

Step-by-Step

PROBLEM: My friend Rohan and I bought snacks. I bought 2 packets of biscuits and 1 packet of chips for ₹50. Rohan bought 1 packet of biscuits and 2 packets of chips for ₹40. What is the cost of one packet of biscuits and one packet of chips?

Step 1: Identify the unknowns. Let 'b' be the cost of one packet of biscuits and 'c' be the cost of one packet of chips.
---Step 2: Write down the information as equations.
My purchase: 2b + c = 50 (Equation 1)
Rohan's purchase: b + 2c = 40 (Equation 2)
---Step 3: From Equation 1, express 'c' in terms of 'b': c = 50 - 2b.
---Step 4: Substitute this value of 'c' into Equation 2:
b + 2(50 - 2b) = 40
b + 100 - 4b = 40
---Step 5: Solve for 'b':
100 - 3b = 40
100 - 40 = 3b
60 = 3b
b = 60 / 3
b = 20
---Step 6: Now that we know b = 20, substitute it back into c = 50 - 2b to find 'c':
c = 50 - 2(20)
c = 50 - 40
c = 10
---Answer: The cost of one packet of biscuits is ₹20 and the cost of one packet of chips is ₹10.

Why It Matters

Understanding two unknowns helps you solve complex problems in Maths, Science, and even in daily life. Engineers use this to design buildings, programmers use it in AI algorithms, and scientists use it to model physical systems. It's a fundamental skill for many exciting careers!

Common Mistakes

MISTAKE: Trying to solve for two unknowns with only one piece of information (one equation). | CORRECTION: You usually need as many pieces of information (equations) as you have unknowns to find a unique solution.

MISTAKE: Using the same letter for two different unknowns. | CORRECTION: Always use different letters (like x and y, or b and c) to represent different unknown quantities to avoid confusion.

MISTAKE: Making calculation errors when substituting one unknown into another equation. | CORRECTION: Double-check your arithmetic, especially when multiplying or subtracting negative numbers, to ensure accuracy.

Practice Questions

Try It Yourself

QUESTION: A farmer has some chickens and some goats. He counts 10 heads and 26 legs in total. How many chickens and how many goats does he have? (Hint: Chickens have 1 head and 2 legs, goats have 1 head and 4 legs) | ANSWER: 7 chickens and 3 goats

QUESTION: The sum of two numbers is 15. Their difference is 3. What are the two numbers? | ANSWER: The numbers are 9 and 6.

QUESTION: At a school fair, 3 tickets for a game and 2 tickets for a ride cost ₹110. If 2 tickets for the game and 3 tickets for the ride cost ₹140, what is the cost of one game ticket and one ride ticket? | ANSWER: Game ticket = ₹10, Ride ticket = ₹40

MCQ

Quick Quiz

Which of these situations involves having two unknowns?

Finding the total number of students in a class.

Calculating the area of a square when you know its side length.

Determining the price of a pen and a notebook when given their combined cost and individual price difference.

Measuring the temperature of water.

The Correct Answer Is:

Option C requires finding two different values (price of pen, price of notebook) using two pieces of information. The other options involve finding only one value or already have all necessary information.

Real World Connection

In the Real World

When a delivery app like Swiggy or Zomato calculates the best route for its riders, it often has to solve problems with multiple unknowns, like different traffic conditions and delivery times for various orders. Similarly, in cricket analytics, predicting player performance might involve two unknowns like strike rate and average, each influencing the outcome.

Key Vocabulary

Key Terms

UNKNOWN: A quantity whose value is not known | VARIABLE: A symbol (usually a letter) representing an unknown quantity | EQUATION: A statement that two mathematical expressions are equal | SYSTEM OF EQUATIONS: A set of two or more equations with the same unknowns

What's Next

What to Learn Next

Next, you can learn about 'Solving Systems of Linear Equations'. This will teach you different methods, like substitution and elimination, to efficiently find the values of two or more unknowns. It's a super useful skill!