Represent the situation algebraically and graphically

Video Explanation

Watch the video explanation below:

Given

Akhila went to a fair in her village.

• Let the number of Giant Wheel rides = x
• The number of Hoopla games = x/2
• Cost of one Giant Wheel ride = ₹3
• Cost of one Hoopla game = ₹4
• Total amount spent = ₹20

To Represent

• The situation algebraically
• The situation graphically

Algebraic Representation

Cost of Giant Wheel rides = 3x

Cost of Hoopla games = 4(x/2) = 2x

Total cost:

3x + 2x = 20

5x = 20

x = 4

Interpretation

Number of Giant Wheel rides = 4

Number of Hoopla games = 4/2 = 2

Graphical Representation

The algebraic equation obtained is:

5x = 20

or,

x = 4

Steps to Draw the Graph

• Take x on the horizontal axis.
• Take y = 5x on the vertical axis.
• Plot points satisfying y = 5x such as (0, 0), (2, 10), (4, 20).
• Draw a straight line passing through these points.
• Draw a horizontal line y = 20.
• The point of intersection gives the solution.

The two lines intersect at the point (4, 20).

Final Answer

The algebraic equation is:

5x = 20

The graphical solution shows:

x = 4

So, Akhila enjoyed:

• 4 Giant Wheel rides
• 2 games of Hoopla

Conclusion

Thus, the given situation is correctly represented both algebraically and graphically.