Question

montraie is going to a carnival that has games and rides. each game costs $1 and each ride costs $3.75. montraie spent $17.50 altogether on 12 games and rides. determine the number of games montraie played and the number of rides montraie went on.

Explanation:

Step1: Define variables

Let \( g \) be the number of games and \( r \) be the number of rides. We know two equations:

1. \( g + r = 12 \) (total number of games and rides)
2. \( 1g + 3.75r = 17.50 \) (total cost equation)

Step2: Solve the system of equations

From the first equation, we can express \( g \) as \( g = 12 - r \). Substitute this into the second equation:
\( (12 - r) + 3.75r = 17.50 \)

Step3: Simplify and solve for \( r \)

Simplify the left - hand side: \( 12+2.75r = 17.50 \)
Subtract 12 from both sides: \( 2.75r=17.50 - 12=5.50 \)
Divide both sides by 2.75: \( r=\frac{5.50}{2.75} = 2 \)

Step4: Solve for \( g \)

Substitute \( r = 2 \) into \( g = 12 - r \): \( g=12 - 2=10 \)

Answer:

Montraie played 10 games and went on 2 rides.