Question

Akhila went to a fair in her village. She wanted to enjoy rides on the Giant Wheel and play Hoopla (a game in which you throw a rig on the items in the stall, and if the ring covers any object completely you get it). The number of times she played Hoopla is half the number of rides she had on the giant wheel. Each ride costs ₹3 and a game of hoopla costs ₹4. If she spent ₹20 in the fair, represent this situation algebraically and graphically.

Answer 1

Let ‘x’ be the number of rides Akhila had on the giant wheel. 

And, let ‘y’ be the number of times she played Hoopla. 

From the question we can write the below pair of equations. 

y = (\(\frac{1}{2}\))x 

⇒ x -2y = 0……. (i) 

3x + 4y = 20……. (ii) 

To represent these equations graphically we need at least two solutions for each (i) and (ii). 

And let’s put them in a table for each: 

x	0	2
y = (\(\frac{1}{2}\))x	0	1

For equation (ii),

x	0	\(\frac{20}{3}\)	4
\(y = \frac{(20-3x)}{4}\)	5	0	2

When: 

The solution of the variable is zero; the equation can be solved easily. Putting x =0 in equation (ii) we get 

4y = 20 

⇒ y = 5 

Similarly putting y = 0 in equation (ii) we get 

3x = 20

⇒x = 20/3 but it is not an integer so it is not easy to plot on graph paper.

So, we chose y=2 which gives x =4 as an integer value. 

The above can be plotted in a graph as below:

We can observe that the two lines represents the equations (i) and (ii) intersect at a single point.