Question

Arianna and her friend Grace are going to a carnival that has games and rides. Arianna played 6 games and went on 3 rides and spent a total of $27. Grace played 2 games and went on 9 rides and spent a total of $41. Determine the cost of each game and the cost of each ride.

Answer 1

Rides cost $4

Games cost $2.50

Explanation:

Let g = cost of games

Let r = cost of rides

6g + 3r = 27

2g + 9r = 41 Multiple this through by -3 and then add to the equation above.

-3(2g + 9r) = (41) -3

-6g - 27r = - 123

6g + 3r = 27

-24r = -96 Divide both sides by -24

r = 4 This is the cost of the rides.

Plug is 4 for r in either of the two original equations to solve for g

6g + 3r = 27

6g + 3(4) = 27

6g + 12 = 27 Subtract 12 from both sides

6g = 15 Divide both sides by 6

g = 2.5 This is the cost of the games.