Case Based Questions: Expressions using Letter-Numbers | Mathematics (Ganita Prakash) Class 7 - New NCERT PDF Download

Q1: Read the source and answer the question that follows

Parthiv was playing with matchsticks and observed a pattern when he arranged them into L-shaped designs. He noticed that for every L-shape, he needed 2 matchsticks. As the number of L-shapes increased, the number of matchsticks followed a clear pattern:

• 1 L-shape needed 2 matchsticks.

• 2 L-shapes needed 4 matchsticks.

• 5 L-shapes needed 10 matchsticks.

• 45 L-shapes needed 90 matchsticks.

The number of matchsticks used is always 2 times the number of L-shapes. Let the number of L-shapes be represented by 'n'. The total number of matchsticks can be written as an algebraic expression:
Number of matchsticks = 2 × n

Q1: How many matchsticks are needed for 8 L-shapes?
(a) 14
(b) 16
(​​​​​c) 18
(d) 20

Ans: (b) 16
Explanation: Number of matchsticks = 2 × 8 = 16.

Q2: Write an expression for the number of matchsticks needed for 'n' L-shapes.

Ans: The algebraic expression is:
Number of matchsticks = 2 × n, where 'n' is the number of L-shapes.

Q3: How does the number of matchsticks increase as the number of L-shapes increases?

Ans: The number of matchsticks increases linearly, as the number of matchsticks is always twice the number of L-shapes. This relationship can be expressed as an algebraic expression 2n, where 'n' is the number of L-shapes.

Q2: Read the source and answer the question that follows

Rani went shopping and bought coconuts and jaggery. The cost of a coconut is ₹35 and the cost of jaggery is ₹60 per kilogram. Let the number of coconuts be 'c' and the number of kilograms of jaggery be 'j'. The total cost can be represented by the algebraic expression:

Total cost = (c × 35) + (j × 60)

Q1: If Rani buys 10 coconuts and 5 kg of jaggery, what will be her total cost?
(a) ₹650
(b) ₹700
(c) ₹600
​(d) ₹750

Ans: (a) ₹650
Explanation: Total cost = (10 × 35) + (5 × 60) = 350 + 300 = ₹650.

Q2: Write an algebraic expression to represent the total cost of 'c' coconuts and 'j' kg of jaggery.
Ans: The algebraic expression is:
Total cost = (c × 35) + (j × 60), where 'c' is the number of coconuts and 'j' is the number of kilograms of jaggery.

Q3: Read the source and answer the question that follows

Aditya is planning to buy some books and stationery for the upcoming semester. He buys 3 books, each costing ₹100, and 5 notebooks, each costing ₹50. How much will he spend in total?

To express this situation algebraically, let:

• b = cost of each book

• n = cost of each notebook

The total cost for books and notebooks can be written as the expression:

Total cost = (3 × b) + (5 × n)

If b = ₹100 and n = ₹50, substitute the values to calculate the total:

Total cost = (3 × 100) + (5 × 50) = 300 + 250 = ₹550.

Q1. If Aditya wants to buy 10 more books, how will the total cost change? Write the new expression.

Ans: If Aditya buys 10 more books, the new expression will be:
Total cost = (3 × 100) + (5 × 50) + (10 × 100) = 300 + 250 + 1000 = ₹1550.

Q2. Why is it helpful to use variables (letters) in situations like calculating the total cost of books and notebooks?

Ans: Using variables like letters allows us to generalize the situation, making it easier to calculate total costs in different scenarios. Instead of repeatedly writing the same calculations, we can substitute values for the variables and quickly calculate the total cost for different numbers of books or notebooks