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 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.

Answer 1

x = 4

Step-by-step explanation:

Given: Each Giant wheel ride costs Rs. 3. Each game of Hoopla costs Rs. 4. Akhila spent Rs. 20 in total. The number of times she played Hoopla is half the number of rides she had on the Giant Wheel.

Solution: Let number of giant wheel rides by x, then the number of games of hoopla will be x/2

 So 3x + 4(x/2) = 20

   3x + 2x = 20

   5x = 20

    x = 4

Number of Giant wheel rides = 4 at the cost of 3 each, she spent Rs. 12 on this game.

Number of games of Hoopla   = 2 at the cost of 4 each, she spent Rs. 8 on this game.

Graphically x = 4 will be a vertical line 4 units to the right of the origin and will be parallel to the y - axis.

Answer 2

Concept :

To draw the graph of a linear equation in two variable a series of steps to be followed which is given below:

• Step I:Obtain the linear equation.  Let the equation be  ax + by + c = 0
• Step II: Express one unknown quantity in terms of other here. Express y in terms of x to get y = - (ax + c /b)
• Step III: For any two values of x, calculate the corresponding values of y  from the expression in step II to obtain two solutions say (x1, y1 and( x2 ,y2)
• Step IV: plot the points  (x1, y1 and( x2 ,y2)  on graph paper on a suitable scale.
• Step V:Draw a  line passing through points marked in step IV. The line so obtained is the graph of the equation  ax + by + c = 0  

 

Given: Akhila went to a fair in her village.  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. she spent Rs 20 in the fair.

Solution :

Let the number of times Akhila played Hoopla be x and number of times Akhila played Giant wheel be y.

Condition: 1  

y = ½ x

x = 2y

x – 2y = 0 ………..(1)

Condition:2  

3x + 4y = 20 ………..(2)

Hence , algebraically it is represented by :

x – 2y = 0 and 3x + 4y = 20

Table and the Graph ( Geometrically) of the given  systems of equations are  in the  attachment below :  

x – 2y = 0 , passes through (0, 0) and (2,1)

3x − y = 3 passes through (0,5) and (4, 2)

The points are A(0, 0); B(0, 5) and P(0, 5) ; Q(4, 2)

Hope this answer will help you…

 

Some more questions from this chapter :  

 Solve the following systems of equations graphically:

x+y=3

2x+5y=12

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Solve the following systems of equations graphically:

x-2y=5

2x+3y=10

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