Question

Akhila went to a fair with Rs. 200 where she wanted to have rides on the Giant Wheel and play Hoopla. 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 cost Rs. 4, Express the situations algebraically.

Answer 1

$\large\underline{\sf{Solution-}}$

Let suppose that

Number of rides on Giant wheel be 'x'

and

Number of play on Hoopla be 'y'

Now,

According to first condition,

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

$\rm :\longmapsto\:y = \dfrac{x}{2}$

or

$\rm :\longmapsto\:x = 2y$

or

$\red{\rm :\longmapsto\:x - 2y = 0 - - - (1)}$

According to second condition,

Each ride costs Rs. 3 and a game of Hoopla cost Rs. 4 and Akhila with have Rs 200.

So,

Amount spend on GIANT WHEEL = 3X

and

Amount spend on game of HOOPLA = 4y

So,

$\red{\rm :\longmapsto\:3x + 4y = 200 - - - - (2)}$

So, algebraically equations are

$\red{\rm :\longmapsto\:x - 2y = 0 - - - (1)}$

and

$\red{\rm :\longmapsto\:3x + 4y = 200 - - - - (2)}$

Additional Information :-

There are 4 methods to solve this type of pair of linear equations.

1. Method of Substitution

2. Method of Eliminations

3. Method of Cross Multiplication

4. Graphical Method

What is Method of Eliminations

To solve systems using elimination, follow this procedure:

The Elimination Method

Step 1: Multiply each equation by a suitable number so that the two equations have the same leading coefficient.

Step 2: Subtract the second equation from the first to eliminate one variable

Step 3: Solve this new equation for other variable.

Step 4: Substitute the value of variable thus evaluated into either Equation 1 or Equation 2 and get the value other variable.