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 ring on the items kept in a stall and if the ring covers any object completely you get it ) if the number of times she played hoopla is half the number of times she rides the giant wheel if each ride cost Rs. 3 and a game of hoopla cost Rs. 4 and she spent Rs. 20 in the fair represent the situation algebraically and graphically.
Given:
Number of times she played hoopla is half the number of times she rides the giant wheel.
Cost of each ride = Rs. 3
Cost of a game of hoopla = Rs. 4
Total money Akhila spent = Rs. 20
To do: Here we have to represent the situation algebraically and graphically.
Solution:
Let the number of rides be = $x$
Let number of game played = $y$
Now,
(Cost of each ride) $\times$ (No. of rides) $+$ (Cost of each game) $\times$ (No. of games) = Total money spent by Akhila
$3x\ +\ 4y\ =\ 20$ ....(i)
Number of times she played hoopla is half the number of times she rides the giant wheel:
$\frac{x}{2}\ =\ y$
$x\ =\ 2y$
$2y\ -\ x\ =\ 0$ ....(ii)
Using equation (i):
$3x\ +\ 4y\ =\ 20$
$x\ =\ \frac{20\ -\ 4y}{3}$
$(x,\ y)$ = (0, 4) and (4, 2).
Using equation (ii):
$2y\ -\ x\ =\ 0$
$x\ =\ 2y$
$(x,\ y)$ = (4, 2) and (2, 1)
![](/assets/questions/media/113574-21729-1603094935.png)
Solution of these two equations is where they intersect each other (point A). So,
$\mathbf{(x,\ y)}$ = (4, 2)
Therefore,
Number of rides be = $x$ = 4
Number of game played = $y$ = 2
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