Arianna and her friend Alexa are going to a carnival that has games and rides. Arianna played 6 games and went on 2 rides and spent a total of $21.50. Alexa played 10 games and went on 7 rides and spent a total of $53.25. Write a system of equations that could be used to determine the cost of each game and the cost of each ride. Define the variables that you use to write the system.

Answer:

6x + 2y = 21.50 equation (i)

10x + 7y = 53.25 equation (ii)

Where x represent game and y represent ride.

Cost of 1 game = $2

Cost of 1 ride = $4.75

Step-by-step explanation:

To solve this question, we have to write two set of equations, each giving details of account of the two parties involved.

Let x represent games

Let y represent rides

So, with Arianna,

6x + 2y = 21.50.......equation (i)

With Alexa,

10x + 7y = 53.25 ........equation(ii)

We can solve this equations and go ahead to find the cost of ride and game using simultaneous equation

From equation (i)

6x + 2y = 21.50

Make x the subject of formula,

6x = 21.50 - 2y

x = (21.50 - 2y) / 6 ......equation (iii)

Put equation (iii) into equation (ii)

10x + 7y = 53.25

10 [(21.50 - 2y) / 6] + 7y = 53.25

(215 - 20y) / 6 + 7y = 53.25

(215 - 20y + 42y) / 6 = 53.25

215 + 22y = 53.25 × 6

215 + 22y = 319.5

22y = 319.5 - 215

22y = 104.5

y = 4.75

Put y = 4.75 in either equation (i) or (ii) to find x.

From equation (i)

6x + 2y = 21.50

6x + 2(4.75) = 21.50

6x + 9.5 = 21.50

6x = 21.50 - 9.5

6x = 12

X = 12 / 6

X = 2

Therefore the cost of 1 game is $2 and 1 ride is $4.75

The system of equations are,  \(6x+2y=21.5\) and \(10x+7y=53.25\)

where cost of each game is x dollar and cost of each ride is y dollar.

Let us consider that cost of each game is x dollar and cost of each ride is y dollar.

Since, Arianna played 6 games and went on 2 rides and spent a total of $21.50.

                      \(6x+2y=21.5\)

and Alexa played 10 games and went on 7 rides and spent a total of $53.25.

                    \(10x+7y=53.25\)

Hence, the system of equations are,  \(6x+2y=21.5\) and \(10x+7y=53.25\)

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