Question

unit: solving equations and inequalities
nathan has a $75 budget to rent a car for a day. the daily rental charge is $29.50 and then he will also have to pay $0.55 per mile. how many miles can he drive the car without exceeding his budget? (all partial miles are counted as full miles.)
\bigcirc 82 miles
\bigcirc 136 miles
\bigcirc 83 miles
\bigcirc 25 miles

Explanation:

Step1: Define variables and cost equation

Let \( m \) be the number of miles. The total cost \( C \) is the daily charge plus the cost per mile times miles: \( C = 29.50 + 0.55m \). We know \( C \leq 75 \) (budget). So, \( 29.50 + 0.55m \leq 75 \).

Step2: Solve the inequality for \( m \)

Subtract 29.50 from both sides: \( 0.55m \leq 75 - 29.50 \). Calculate \( 75 - 29.50 = 45.5 \). Then, \( 0.55m \leq 45.5 \). Divide both sides by 0.55: \( m \leq \frac{45.5}{0.55} \approx 82.73 \). Since partial miles count as full, the maximum integer miles is 82.

Answer:

82 miles (the option with "82 miles")