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 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 and graphically.
Let the number of times Akhila played Hoopla be x and number of times she played Giant wheel be y.
Given, number of times she played Hoopla is half the number of rides she had on the Giant Wheel.
⇒ x = 2y
⇒ x – 2y = 0
Each ride costs Rs 3, and a game of Hoopla costs Rs 4 and she spent Rs 20 in the fair.
⇒ 3x + 4y = 20
Thus, algebraically it is represented by :
x – 2y = 0 and 3x + 4y = 20
x – 2y = 0 passes through origin
3x + 4y = 20 passes through (0, 5) and (20/3, 0)