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.

answer: attempt 1 out of 2

montraie played \boxed{} games and went on \boxed{} rides.

Explanation:

Step1: Define variables

Let \( g \) be the number of games and \( r \) be the number of rides. We know two equations: \( g + r = 12 \) (total number of games and rides) and \( 1g + 3.75r = 17.50 \) (total cost). From the first equation, we can express \( g = 12 - r \).

Step2: Substitute into cost equation

Substitute \( g = 12 - r \) into \( g + 3.75r = 17.50 \):
\( (12 - r) + 3.75r = 17.50 \)
Simplify: \( 12 + 2.75r = 17.50 \)

Step3: Solve for \( r \)

Subtract 12 from both sides: \( 2.75r = 5.50 \)
Divide by 2.75: \( r = \frac{5.50}{2.75} = 2 \)

Step4: Solve for \( g \)

Use \( g = 12 - r \): \( g = 12 - 2 = 10 \)

Answer:

Montraie played \(\boldsymbol{10}\) games and went on \(\boldsymbol{2}\) rides.