What is a Formula with One Variable?

S1-SA5-0299

Grade Level:

Class 5

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

Definition

What is it?

A formula with one variable is a mathematical rule or equation that uses only one unknown quantity, represented by a letter like 'x' or 'y'. It helps us find the value of that unknown when we know other numbers in the formula. Think of it like a recipe where you only need to figure out one missing ingredient.

Simple Example

Quick Example

Imagine you buy a packet of samosas. Each samosa costs Rs. 10. If you buy 'n' number of samosas, the total cost would be 10 * n. Here, 'n' is the one variable, and the formula is 'Total Cost = 10 * n'. If you buy 5 samosas, n=5, and the cost is 10 * 5 = Rs. 50.

Worked Example

Step-by-Step

PROBLEM: An auto-rickshaw charges a base fare of Rs. 20 and then Rs. 8 for every kilometer travelled. If the total fare for a trip was Rs. 60, how many kilometers (k) did the auto travel?

Step 1: Write down the formula for total fare. Total Fare = Base Fare + (Rate per km * k)
---Step 2: Substitute the known values into the formula. 60 = 20 + (8 * k)
---Step 3: To find 'k', first subtract the base fare from the total fare. 60 - 20 = 8 * k
---Step 4: This simplifies to 40 = 8 * k
---Step 5: Now, divide both sides by 8 to find 'k'. 40 / 8 = k
---Step 6: Calculate the value of k. k = 5
---ANSWER: The auto-rickshaw travelled 5 kilometers.

Why It Matters

Understanding formulas with one variable is crucial for solving problems in almost all STEM fields, from calculating distances in Physics to mixing chemicals in Chemistry. It's used by engineers to design bridges, by data scientists to analyze trends, and by financial experts to manage money. Mastering this helps you think logically and solve real-world puzzles.

Common Mistakes

MISTAKE: Students often forget to perform operations in the correct order (PEMDAS/BODMAS). For example, in 2 + 3x = 11, they might add 2 and 3 first. | CORRECTION: Always remember to multiply/divide before adding/subtracting. First, subtract 2 from both sides, then divide by 3.

MISTAKE: Not doing the same operation on both sides of the equals sign. For instance, adding 5 to one side but not the other. | CORRECTION: Whatever you do to one side of the equation (add, subtract, multiply, divide), you must do the exact same thing to the other side to keep the equation balanced.

MISTAKE: Confusing the variable with a known number, especially when the variable is on the right side of the equation. Example: 15 = 3 + y, and they think y must be 5 because 15/3=5. | CORRECTION: Remember the variable represents an unknown number. To solve 15 = 3 + y, subtract 3 from 15 to find y, which is 12.

Practice Questions

Try It Yourself

QUESTION: A mobile recharge plan costs Rs. 50 for activation plus Rs. 10 for every GB of data used. If your total bill was Rs. 120, how many GB of data (d) did you use? | ANSWER: d = 7 GB

QUESTION: In a cricket match, Rohit scored 'x' runs. Virat scored twice as many runs as Rohit, plus 10 extra runs. If Virat scored 110 runs, how many runs did Rohit (x) score? | ANSWER: x = 50 runs

QUESTION: A tiffin service charges a monthly fee of Rs. 800. Additionally, they charge Rs. 30 for each extra dish ordered. If a customer's total bill for a month was Rs. 950, how many extra dishes (e) did they order? | ANSWER: e = 5 dishes

MCQ

Quick Quiz

Which of the following is a formula with one variable?

Area = length * width

Perimeter = 2 * (length + width)

Cost = 5 * quantity

Speed = distance / time

The Correct Answer Is:

Option C, 'Cost = 5 * quantity', has only one unknown quantity ('quantity') if '5' is a fixed price. The other options (A, B, D) involve two or more different variables.

Real World Connection

In the Real World

Formulas with one variable are used every day in India! When you check your electricity bill, the total amount is calculated using a formula where the 'units consumed' is the variable. When you plan a trip, you might use a formula to calculate fuel cost, where 'distance' is the variable. Even apps like Swiggy or Zomato use these to calculate your total order price based on the 'number of items' you buy.

Key Vocabulary

Key Terms

VARIABLE: A letter (like x or y) that represents an unknown number or quantity. | FORMULA: A mathematical rule or equation that shows the relationship between different quantities. | EQUATION: A statement that two mathematical expressions are equal. | SOLVE: To find the value of the unknown variable that makes the equation true.

What's Next

What to Learn Next

Great job understanding formulas with one variable! Next, you can explore 'Formulas with Two Variables'. This will help you solve even more complex problems where you need to find two unknown quantities at the same time, building on the strong foundation you've created here.