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 ring on the items kept 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 Rs. 3, and a game of Hoopla costs Rs. 4. If she spent Rs. 20 in the fair, represent this situation algebraically.

Answer 1

Hint: Let the number of rides Akhila enjoyed and the number of games of Hoopla she played be the variables. Now using the conditions given in the question form two equations, one for the relation of the number of rides and the number of games and other for the amount she spent. Solve the equations to get the required answers.

Complete step-by-step answer:

To begin with the solution, we let the number of rides of the giant wheel enjoyed by Akhila be x and the number of games of hoopla she played be y.
Now it is given in the question that the number of times she played Hoopla is half the number of rides she had on the giant wheel.
$\therefore y=\dfrac{x}{2}............(i)$
Now, as each ride of the giant wheel costs Rs. 3, her spending on the ride is 3x, and as the cost of playing per game of hoopla is Rs. 4, so she spent Rs. 4y on Hoopla. Also, it is given that she spent a total amount of Rs. 20. So, the equation we get is:
3x+4y=20
Now we will substitute the value of y from equation (i). On doing so, we get
\[3x+4\times \dfrac{x}{2}=20\]
\[\Rightarrow 5x=20\]
\[\Rightarrow x=4\]
 And as y is half of x, so y=2.
Therefore, she took 4 rides on the giant wheel and played 2 games of Hoopla in the village's fair.

Note: Be careful with the signs and calculations as in such questions, the possibility of making a mistake is either of the sign or a calculation error.