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.

• A. Pencil = Rs 1, Chocolate = Rs 3
• B. Pencil = Rs 2, Chocolate = Rs 3
• C. Pencil = Rs 1, Chocolate = Rs 4
• D. Pencil = Rs 3, Chocolate = Rs 1

Hint:

Even when asked for a graphical solution, always solve the system algebraically on your rough sheet first!
This gives you the exact intersection point \((1, 3)\), ensuring your hand-drawn lines on the graph are perfectly aligned and pass through the correct grid intersections.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
Two people buy items at the same shop:
- Aarush buys 2 pencils and 3 chocolates for Rs 11.
- Tanish buys 1 pencil and 2 chocolates for Rs 7.
We need to represent this situation as a system of linear equations and solve for the individual cost of a pencil and a chocolate.

Step 2: Key Formula or Approach:
1. Let the price of one pencil be Rs \(x\) and the price of one chocolate be Rs \(y\).
2. Formulate the two linear equations:
\[ 2x + 3y = 11 \]
\[ x + 2y = 7 \]
3. To solve graphically, we find coordinates for each line, plot them on a grid, and identify their point of intersection \((x, y)\).

Step 3: Detailed Explanation:
1. Represent the situations as equations:
- For Aarush:
\[ 2x + 3y = 11 \quad \text{--- (Line 1)} \]
- For Tanish:
\[ x + 2y = 7 \quad \text{--- (Line 2)} \]
2. Find coordinates for Line 1 (\(2x + 3y = 11\)):
- If \(x = 1 \implies 2(1) + 3y = 11 \implies 3y = 9 \implies y = 3\). Point: \((1, 3)\).
- If \(x = 4 \implies 2(4) + 3y = 11 \implies 3y = 3 \implies y = 1\). Point: \((4, 1)\).
- If \(x = -2 \implies 2(-2) + 3y = 11 \implies 3y = 15 \implies y = 5\). Point: \((-2, 5)\).
3. Find coordinates for Line 2 (\(x + 2y = 7\)):
- If \(x = 1 \implies 1 + 2y = 7 \implies 2y = 6 \implies y = 3\). Point: \((1, 3)\).
- If \(x = 3 \implies 3 + 2y = 7 \implies 2y = 4 \implies y = 2\). Point: \((3, 2)\).
- If \(x = 5 \implies 5 + 2y = 7 \implies 2y = 2 \implies y = 1\). Point: \((5, 1)\).
4. Describe the graph:
- Plotting these points on a Cartesian grid and drawing straight lines through them shows that both lines intersect exactly at the point \((1, 3)\).
- Therefore, the solution of the system of equations is \(x = 1\) and \(y = 3\).
- This means the cost of one pencil is Rs 1 and the cost of one chocolate is Rs 3.

Step 4: Final Answer:
The price of 1 pencil is Rs 1 and 1 chocolate is Rs 3, which corresponds to option (A).