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, [tex]6x+2y=21.5[/tex] and [tex]10x+7y=53.25[/tex]
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.
[tex]6x+2y=21.5[/tex]
and Alexa played 10 games and went on 7 rides and spent a total of $53.25.
[tex]10x+7y=53.25[/tex]
Hence, the system of equations are, [tex]6x+2y=21.5[/tex] and [tex]10x+7y=53.25[/tex]
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