Alexa played 6 games and went on 9 rides.
To solve the given problem, we need to use the information that each game costs $3 and each ride costs $4, and Alexa spent $54 altogether on 15 games and rides. We can set up two equations to represent this information:
Let x be the number of games Alexa played and y be the number of rides Alexa went on.
Equation 1: (3x + 4y = 54) (total cost of games and rides is $54)
Equation 2: (x + y = 15) (total number of games and rides is 15)
We can solve this system of equations using substitution or elimination. Here, we will use elimination.
Multiplying Equation 2 by 3, we get:
Equation 3: (3x + 3y = 45)
Subtracting Equation 3 from Equation 1, we get:
(3x + 4y - (3x + 3y) = 54 - 45)
(y = 9)
Substituting y = 9 into Equation 2, we get:
(x + 9 = 15)
(x = 6)
Therefore, Alexa played 6 games and went on 9 rides.