Question

you have $20 to spend on taxi fare. the ride costs $5 plus $2.50 per kilometer.
write an inequality to determine the distance in kilometers, d, you can ride for $20.
what is the maximum distance, in kilometers, you can ride for $20?
kilometers

Explanation:

Step1: Define the cost function

The total cost of the taxi ride is the initial cost plus the cost per kilometer times the distance. So the cost \( C \) is \( C = 5 + 2.50d \), where \( d \) is the distance in kilometers. Since we have at most \$20 to spend, the inequality is \( 5 + 2.50d \leq 20 \).

Step2: Solve the inequality for \( d \)

Subtract 5 from both sides: \( 2.50d \leq 20 - 5 \) which simplifies to \( 2.50d \leq 15 \). Then divide both sides by 2.50: \( d \leq \frac{15}{2.50} \). Calculating \( \frac{15}{2.50} = 6 \).

Answer:

The inequality is \( 5 + 2.50d \leq 20 \) and the maximum distance is 6 kilometers.