Question

Valeria is going to a carnival that has games and rides. Each game costs $1.50 and each ride costs $3. Valeria spent $21 altogether on 8 games and rides. Solve a system of equations in order to determine the number of games Valeria played, x, and the number of rides Valeria went on, y.

Answer 1

Let x be the number of games Valeria played and y be the number of rides she went on. Then we can set up a system of equations:

x + y = 8 (because Valeria played 8 games and rides total)

1.5x + 3y = 21 (because each game costs $1.50 and each ride costs $3, and Valeria spent $21 in total)

We can solve for x in the first equation by subtracting y from both sides:

x = 8 - y

Then we can substitute this expression for x into the second equation:

1.5x + 3y = 21

1.5(8 - y) + 3y = 21

12 - 1.5y + 3y = 21

1.5y = 9

y = 6

So Valeria went on 6 rides. We can substitute this value for y back into the first equation and solve for x:

x + y = 8

x + 6 = 8

x = 2

So Valeria played 2 games. Therefore, Valeria played 2 games and went on 6 rides.

Answer 2

The system of equations will be

1.50 x + 3y = 21

x + y = 8

Solve them graphically to get the point (2,6)

The number of games played are 2, and the number of rides she went on are 6.

Explanation: