Question

challenge a family wants to rent a car to go on vacation. company a charges $40.50 and 9¢ per mile. company b charges $55.50 and 15¢ per mile. how much more does company b charge for x miles than company a?
for x miles, company b charges \boxed{} dollars more than company a.
(simplify your answer. use integers or decimals for any numbers in the expression.)

Explanation:

Step1: Find cost of Company A

Company A charges a fixed fee of $40.50 and 9¢ per mile. Convert 9¢ to dollars: \( 9\cancel{\text{¢}} \times \frac{\$1}{100\cancel{\text{¢}}} = \$0.09 \). So cost for \( x \) miles: \( 40.50 + 0.09x \).

Step2: Find cost of Company B

Company B charges a fixed fee of $55.50 and 15¢ per mile. Convert 15¢ to dollars: \( 15\cancel{\text{¢}} \times \frac{\$1}{100\cancel{\text{¢}}} = \$0.15 \). So cost for \( x \) miles: \( 55.50 + 0.15x \).

Step3: Find difference (B - A)

Subtract Company A's cost from Company B's cost:
\( (55.50 + 0.15x) - (40.50 + 0.09x) \)
Simplify: \( 55.50 - 40.50 + 0.15x - 0.09x = 15 + 0.06x \).

Answer:

\( 15 + 0.06x \)