Question

comparing two linear functions (context - graphically)
name 13 -
questions
dassyla is deciding between two truck rental companies. company a charges an initial fee of $40 for the rental plus $0.90 per mile driven. company b charges an initial fee of $20 for the rental plus $1 per mile driven. let a represent the amount company a would charge if dassyla drives x miles, and let b represent the amount company b would charge if dassyla drives x miles. graph each function and determine the number miles driven, x, that would make the cost of each company the same.
(click icons to plot each line. click a line to delete it.)
number of miles driven
answer
answer:
submit answer

Explanation:

Step1: Define Cost Functions

For Company A: Initial fee $45$, rate $0.90$ per mile. So $A = 45 + 0.90x$.
For Company B: Initial fee $90$, rate $1$ per mile. So $B = 90 + 1x$.

Step2: Set Costs Equal

To find when costs are equal, set $A = B$:
$45 + 0.90x = 90 + x$

Step3: Solve for \( x \)

Subtract \( 0.90x \) from both sides:
$45 = 90 + 0.10x$

Subtract $90$ from both sides:
$-45 = 0.10x$

Divide by $0.10$:
$x = \frac{-45}{-0.10} = 450$

Answer:

450