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

Let the price of 1 pencil = Rs x
Let the price of 1 chocolate = Rs y

According to the problem:
Aarush bought 2 pencils and 3 chocolates for Rs 11:
\[ 2x + 3y = 11 \]
Tanish bought 1 pencil and 2 chocolates for Rs 7:
\[ x + 2y = 7 \]

Thus, the pair of linear equations is:
\[ 2x + 3y = 11 \]
\[ x + 2y = 7 \]

Step 1: Solve graphically
Equation 1: 2x + 3y = 11
Find two points:
• If x = 2 → 2(2) + 3y = 11 → 4 + 3y = 11 → y = 7/3
• If x = 1 → 2(1) + 3y = 11 → 3y = 9 → y = 3

So points are (2, 7/3) and (1, 3).

Equation 2: x + 2y = 7
Find two points:
• If x = 1 → 1 + 2y = 7 → y = 3
• If x = 3 → 3 + 2y = 7 → 2y = 4 → y = 2

So points are (1, 3) and (3, 2).

Graphical Observation:
Plot both lines on the same graph.
They intersect at the common point:
\[ (x, y) = (1, 3) \]

Conclusion (Values from the graph):
Price of 1 pencil = Rs 1
Price of 1 chocolate = Rs 3

Final Answer:
• The pair of linear equations is:
\(2x + 3y = 11\)
\(x + 2y = 7\)

• Price of 1 pencil = Rs 1
• Price of 1 chocolate = Rs 3