Represent the situation algebraically and geometrically

Video Explanation

Watch the video explanation below:

Given

• The cost of 2 kg of apples and 1 kg of grapes is ₹160.
• After a month, the cost of 4 kg of apples and 2 kg of grapes is ₹300.

To Represent

• The situation algebraically
• The situation geometrically (graphically)

Algebraic Representation

Let the cost of 1 kg of apples = x rupees

Let the cost of 1 kg of grapes = y rupees

Equation (1)

Cost of 2 kg apples + 1 kg grapes = 160

2x + y = 160

Equation (2)

Cost of 4 kg apples + 2 kg grapes = 300

4x + 2y = 300

Thus, the algebraic equations are:

2x + y = 160   …(1)

4x + 2y = 300   …(2)

Geometrical (Graphical) Representation

Step 1: Convert Equations into a Suitable Form

Equation (1): 2x + y = 160

Equation (2): 4x + 2y = 300

Step 2: Prepare Tables of Values

For Equation (1): 2x + y = 160

If x = 0, then y = 160

If y = 0, then x = 80

Points: (0, 160) and (80, 0)

For Equation (2): 4x + 2y = 300

If x = 0, then y = 150

If y = 0, then x = 75

Points: (0, 150) and (75, 0)

Step 3: Draw the Graph

• Draw X-axis and Y-axis on graph paper.
• Plot the points (0,160) and (80,0) and join them to get the graph of equation (1).
• Plot the points (0,150) and (75,0) and join them to get the graph of equation (2).

Observation

The two straight lines intersect at one point, showing that the given situation has a unique solution.

Conclusion

Thus, the given situation of the cost of apples and grapes has been correctly represented both algebraically and geometrically.