CBSE Class 7 Maths: Simple Equations Ex 4.4 NCERT

Understanding Word Problems in Simple Equations

In previous exercises, you might have solved equations that were already given to you, like 'x + 5 = 10'. Now, think of a situation where someone tells you, "If you add 5 to my secret number, you get 10." This is a word problem! The main goal of Exercise 4.4 is to equip you with the skills to convert such verbal statements into algebraic equations and then solve them. This process involves careful reading, identifying the unknown quantity, assigning a variable (like 'x' or 'y') to it, and then forming the equation based on the relationships described.

Word problems are incredibly important because they connect abstract mathematical concepts to real-life scenarios. They help you develop logical thinking, analytical skills, and the ability to model complex situations mathematically. Don't worry if it seems challenging at first; with practice, you'll find it quite enjoyable to unravel these numerical riddles!

Steps to Form and Solve Equations from Word Problems

1. Step 1: Read the Problem Carefully — Read the entire word problem at least twice. Understand what information is given and what you are asked to find. Identify the 'unknown' quantity. For example, if the problem states, "The sum of a number and 7 is 15," the unknown is 'a number'.
2. Step 2: Assign a Variable to the Unknown — Choose a letter (like x, y, a, b, etc.) to represent the unknown quantity. This makes it easier to write the mathematical expression. Following our example, let 'x' be the unknown number.
3. Step 3: Translate Keywords into Mathematical Operations — Look for keywords that indicate specific mathematical operations: 'Sum', 'increased by', 'more than', 'added to' mean addition (+) 'Difference', 'decreased by', 'less than', 'subtracted from' mean subtraction (-) 'Product', 'times', 'multiplied by' mean multiplication () 'Quotient', 'divided by', 'per' mean division (/) 'Is', 'equals', 'gives', 'results in' mean equality (=) For our example, 'sum of a number and 7' means 'x + 7', and 'is 15' means '= 15'.
4. Step 4: Formulate the Equation — Combine the variable and operations to write a complete algebraic equation. Using our running example: x + 7 = 15. This is the equation you need to solve.
5. Step 5: Solve the Equation — Use the techniques you've learned for solving simple equations (transposing terms, inverse operations) to find the value of the variable. For x + 7 = 15, transpose 7 to the right side: x = 15 - 7, so x = 8.
6. Step 6: Verify Your Answer (Optional but Recommended) — Substitute the value you found back into the original word problem or the formed equation to check if it satisfies the conditions. If x = 8, then 8 + 7 = 15, which is true. So, your answer is correct!

Solved Examples of Word Problems

• Example 1: If you subtract 5 from 6 times a number, you get 7. Solution: 1. Identify unknown: The number. 2. Assign variable: Let the number be 'y'. 3. Formulate equation: "6 times a number" means 6y. "subtract 5 from 6 times a number" means 6y - 5. "you get 7" means = 7. So, the equation is: 6y - 5 = 7. 4. Solve the equation: 6y - 5 = 7 Add 5 to both sides (or transpose -5): 6y = 7 + 5 6y = 12 Divide both sides by 6: y = 12 / 6 y = 2 5. Verify: 6 * 2 - 5 = 12 - 5 = 7. The answer is correct. Final Answer: The number is 2.
• Example 2: Three-fourths of a number increased by 6 is 15. Solution: 1. Identify unknown: The number. 2. Assign variable: Let the number be 'n'. 3. Formulate equation: "Three-fourths of a number" means (3/4)n. "increased by 6" means + 6. "is 15" means = 15. So, the equation is: (3/4)n + 6 = 15. 4. Solve the equation: (3/4)n + 6 = 15 Subtract 6 from both sides: (3/4)n = 15 - 6 (3/4)n = 9 Multiply both sides by 4/3 (the reciprocal of 3/4): n = 9 (4/3) n = (9 4) / 3 n = 36 / 3 n = 12 5. Verify: (3/4) 12 + 6 = 3 3 + 6 = 9 + 6 = 15. The answer is correct. Final Answer: The number is 12.

Exam Tip: Avoiding Common Mistakes in Word Problems

Solving word problems requires precision. Here are some tips to avoid common pitfalls:

• Misinterpreting Keywords: Carefully distinguish between phrases like "5 less than a number" (which is x - 5) and "a number less than 5" (which could be 5 - x, though the former is more common in simple scenarios). Always read carefully!
• Incorrect Equation Formulation: Double-check your equation against the original problem statement. Does it accurately represent all the information given? A common mistake is to mix up which operation applies to which part of the phrase.
• Calculation Errors: Once you have the equation, take your time solving it. Basic arithmetic errors can lead to an incorrect final answer, even if your equation was perfectly formed.
• Not Answering the Question: Sometimes, the problem asks for something specific, not just the value of the variable. For instance, if 'x' is the number of boys, and the question asks for the number of girls, you might need to perform an extra step after finding 'x'. Always reread the question to ensure your final answer is what was asked for.
• Verification: Always try to substitute your final answer back into the original word problem (not just the equation) to see if it makes sense. This helps catch most errors.

Practice Questions with Solutions

• Q: If you add 4 to eight times a number, you get 60. Find the number. A: Step 1: Let the number be 'x'. "Eight times a number" is 8x. "Add 4 to eight times a number" is 8x + 4. "You get 60" means = 60. So, the equation is 8x + 4 = 60. Step 2: Solve the equation: 8x + 4 = 60 8x = 60 - 4 8x = 56 x = 56 / 8 x = 7 Final answer: The number is 7.
• Q: One-fifth of a number minus 4 gives 3. Find the number. A: Step 1: Let the number be 'y'. "One-fifth of a number" is (1/5)y. "Minus 4" is - 4. "Gives 3" means = 3. So, the equation is (1/5)y - 4 = 3. Step 2: Solve the equation: (1/5)y - 4 = 3 (1/5)y = 3 + 4 (1/5)y = 7 y = 7 * 5 y = 35 Final answer: The number is 35.
• Q: Reena thinks of a number. If she adds 19 to it and divides the sum by 5, she gets 8. What is the number? A: Step 1: Let the number Reena thinks of be 'z'. "She adds 19 to it" means z + 19. "Divides the sum by 5" means (z + 19) / 5. "She gets 8" means = 8. So, the equation is (z + 19) / 5 = 8. Step 2: Solve the equation: (z + 19) / 5 = 8 z + 19 = 8 * 5 z + 19 = 40 z = 40 - 19 z = 21 Final answer: The number is 21.
• Q: The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. If the highest score is 87, what is the lowest score? A: Step 1: Let the lowest marks be 'L'. "Twice the lowest marks" is 2L. "Twice the lowest marks plus 7" is 2L + 7. "The highest score is 87" means = 87. So, the equation is 2L + 7 = 87. Step 2: Solve the equation: 2L + 7 = 87 2L = 87 - 7 2L = 80 L = 80 / 2 L = 40 Final answer: The lowest score is 40.

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