Victor goes to the fair for the rides. The fair in his town is small, so it only has two rides. The ferris wheel costs $2.50 to ride and the ride lasts 7 minutes. The merry-go-round costs $3.00 to ride and the ride lasts 4 minutes. He has $30 and one hour to ride rides. How many times can he ride each ride? write an inequality to represent the situation

Answer 1

Let \( x \) represent the number of times Victor rides the ferris wheel, and \( y \) represent the number of times he rides the merry-go-round.

Costs:

1. The cost for riding the ferris wheel is $2.50, so the total cost for \( x \) rides is \( 2.50x \).
2. The cost for riding the merry-go-round is $3.00, so the total cost for \( y \) rides is \( 3.00y \).

Time:

1. Each ride on the ferris wheel lasts 7 minutes, so the total time for \( x \) rides is \( 7x \) minutes.
2. Each ride on the merry-go-round lasts 4 minutes, so the total time for \( y \) rides is \( 4y \) minutes.

Constraints:

1. The total money spent cannot exceed $30: \[ 2.50x + 3.00y \leq 30 \]

2. The total time spent cannot exceed 60 minutes (1 hour): \[ 7x + 4y \leq 60 \]

Putting it all together, the inequalities representing the situation are:

\[ \begin{align*} 2.50x + 3.00y & \leq 30 \quad \text{(cost constraint)} \ 7x + 4y & \leq 60 \quad \text{(time constraint)} \ x, y & \geq 0 \quad \text{(non-negativity constraints)} \end{align*} \]

Hence, these inequalities define the feasible region for the number of rides Victor can take on the ferris wheel and the merry-go-round given his budget and time constraints.