Algebraic and Graphical Representation Using Linear Equation in Two Variables

Video Explanation

Question

Akhila went to a fair in her village. She enjoyed rides on the Giant Wheel and played Hoopla. The number of times she played Hoopla is half the number of rides she had on the Giant Wheel. Each ride costs ₹3 and each game of Hoopla costs ₹4. If she spent ₹20 in the fair, represent the situation algebraically and graphically.

Solution

Step 1: Define the Variables

Let the number of Giant Wheel rides be \(x\).

Let the number of Hoopla games be \(y\).

Step 2: Form the Linear Equations

According to the question:

The number of Hoopla games is half the number of Giant Wheel rides:

\[ y = \frac{x}{2} \]

Cost of Giant Wheel rides = ₹3 per ride

Cost of Hoopla games = ₹4 per game

Total expenditure is ₹20:

\[ 3x + 4y = 20 \]

Thus, the required linear equation in two variables is:

\[ 3x + 4y = 20 \]

Step 3: Graphical Representation

To draw the graph of the equation \(3x + 4y = 20\), find two solutions.

Table of Values

x	y
0	5
4	2

Plot the points \((0,5)\) and \((4,2)\) on the graph.

Join these points to obtain a straight line.

Conclusion

The situation is represented algebraically by the linear equation:

\[ \boxed{3x + 4y = 20} \]

The graph of this equation is a straight line passing through \((0,5)\) and \((4,2)\).

Hence, the given situation is represented both algebraically and graphically using a linear equation in two variables.