Question

Aarush bought 2 pencils and 3 chocolates for Rs 11 and Tanish bought 1 pencil and 2 chocolates for Rs 7 from the same shop. Represent this situation in the form of a pair of linear equations. Find the price of 1 pencil and 1 chocolate, graphically.

Hint:

While solving graphically, choose values for \( x \) that result in whole numbers for \( y \) to make plotting more accurate and easier.

Answer 1

Step 1: Understanding the Concept:
We need to form two equations based on the cost of items and find their intersection point on a graph.
Step 2: Key Formula or Approach:
Let the price of one pencil be \( x \) and the price of one chocolate be \( y \).
According to Aarush's purchase: \( 2x + 3y = 11 \) (Equation 1)
According to Tanish's purchase: \( x + 2y = 7 \) (Equation 2)
Step 3: Detailed Explanation:
To plot these graphically, find at least two points for each line:
For \( 2x + 3y = 11 \):
If \( x = 1 \), then \( 2(1) + 3y = 11 \implies 3y = 9 \implies y = 3 \). Point: \( (1, 3) \).
If \( x = 4 \), then \( 2(4) + 3y = 11 \implies 3y = 3 \implies y = 1 \). Point: \( (4, 1) \).
For \( x + 2y = 7 \):
If \( y = 3 \), then \( x + 2(3) = 7 \implies x = 1 \). Point: \( (1, 3) \).
If \( y = 2 \), then \( x + 2(2) = 7 \implies x = 3 \). Point: \( (3, 2) \).
When plotted on a graph, the two lines intersect at the point \( (1, 3) \).
This intersection point represents the solution where \( x = 1 \) and \( y = 3 \).
Step 4: Final Answer:
The price of 1 pencil is Rs 1 and the price of 1 chocolate is Rs 3.