Introduction

You must have come across situations like the one given below: 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).

The number of times she played Hoopla is half the number of rides she had on the Giant Wheel.

If each ride costs Rs. 3, and a game of Hoopla costs Rs. 4, how would you find out the number of rides she had and how many times she played Hoopla, provided she spent Rs. 20.

May be you will try it by considering different cases. If she has one ride, is it possible?

May be you will try it by considering different cases. If she has one ride, is it possible?

Is it possible to have two rides? And so on. Or you may use the knowledge of linear equations in two variables which we have already learnt about.

Let us try this approach.

Let's denote the number of rides that Akhila had by 'x', and the number of times she played Hoopla by 'y'. Now the situation can be represented by the two equations:

No. of times she played Hoopla = 122

No. of rides in gaint wheel (y) = 123 × -------------- (1)

Cost of each ride on giant wheel × No. of rides on giant wheel + Cost of playing Hoopla × No. of Hoopla played = Total amount.

× + y = 20------------- (2)

Now, how can we find the solutions of this pair of equations? We will be learning that in this chapter.