Question

Kaylee is going to a carnival that has games and rides. Each game costs $1.25 and each ride costs $2.50. Kaylee spent $12.50 altogether at the carnival and the number of rides she went on is twice the number of games she played. Graphically solve a system of equations in order to determine the number of games Kaylee played, x, and the number of rides Kaylee went on, y

Answer 1

To graphically solve a system of equations, we can plot the equations on a coordinate plane and find the point of intersection, which represents the solution to the system.

The first equation represents the total cost of the games, which is:

x(1.25) = 1.25x

The second equation represents the total cost of the rides, which is:

y(2.50) = 2.50y

The third equation represents the total cost of all games and rides, which is:

x(1.25) + y(2.50) = 12.50

We can also represent the fourth equation as the number of rides she went on is twice the number of games she played:

y = 2x

We can plot the first equation on the coordinate plane by treating x as the x-coordinate and 1.25x as the y-coordinate. We can plot the second equation in the same way, treating x as the x-coordinate and 2.5y as the y-coordinate.

We can plot the third equation as a line by treating x as the x-coordinate and 12.5-1.25x-2.5y as the y-coordinate.

Finally, we can plot the fourth equation as a line by treating x as the x-coordinate and 2x as the y-coordinate.

We can then find the point of intersection of the three lines, which represents the solution to the system of equations.

The point of intersection is the point (5,10) which means that Kaylee played 5 games and went on 10 rides.