Question

Grace is going to a carnival that has games and rides. Each game costs $1.50 and each ride costs $2.50. Grace spent $16.50 altogether at the carnival and the number of games she played is twice the number of rides she went on. Write a system of equations that could be used to determine the number of games Grace played and the number of rides Grace went on. Define the variables that you use to write the system.

Answer 1

# of Rides: 3

# of Games: 6

Explanation:

First try any possible combinations of games *2 more than rides.

Ex: 1&2, 2&4, 3&6, 4&8

2.50*3 = $7.50

1.50*6 = $9.00

7.50 + 9 = $16.50

If # of rides = r and # of games = g, equation:

16.50 = 2.50r + 1.50g

Answer 2

• g=games; r=rides
• 1.5g +2.5r = 16.5
• g = 2r

Explanation:

Let g and r represent the numbers of games played and rides ridden, respectively. Then the system can be written ...

1.50g +2.50r = 16.50 . . . . . total amount spent

g = 2r . . . . . . . . . . . . . . . . . . relationship of games to rides