Question

Suraj and Aditya bought a certain number of pencils that cost Rs 3 each. The number of pencils that Suraj bought is 10 greater than 4 times the number of pencils that Aditya bought. The total cost of pencils that Suraj bought is Rs 162. Find the number of pencils that Aditya bought.

• A. 38
• B. 16
• C. 11
• D. 54

Answer 1

The correct option is C 11

Concept-map across grades: This question is from Grade 7 topic: Applications of solving linear equations It connects to Grade 8 topic: Linear equation in one variable Ability to address the challenges posed in this question could impact topics in higher grades, like Linear equation in two variables.

Let the number of pencils that Aditya bought be x.

Given, the number of pencils that Suraj bought is 10 more than 4 times the number of pencils Aditya bought.

Now, 4 times the number of pencils with Aditya = 4x 10 more than 4x = 4x + 10.

Given, each pencil costs ₹3.

So, the cost of 4x+10 pencils = 3(4x+10)

But it is given that the cost of 4x+10 pencils is ₹162.
=> 3(4x+10) = 162
=> 4x + 10 = 162/3 = 54
=> 4x = 54 - 10 = 44
=> x = 44/4 = 11

Thus, Aditya has 11 pencils.

Each incorrect option in the question refers to specific gaps in learning: a: Understanding the given question statement to convert it into the correct algebraic expression. Number of pencils is equated to total cost of pencils which is incorrect. Total cost of pencils is 3 x number of pencils. b: Writing the correct algebraic expression based on the statement given. Given statement, 10 greater than 4 times the number of pencils is written as 4x - 10 which is incorrect, correct expression is 4x + 10. d: Understanding the given question statement to find the total number of pencils. To calculate the number of pencils, Total cost of pencils is divided by the cost per pencil, which is incorrect. Instead, total cost should be divided by number of pencils.