Question

Makayla is deciding between two truck rental companies. Company A charges an initial fee of $95 for the rental plus $1 per mile driven. Company B charges an initial fee of $75 for the rental plus $2 per mile driven. Let AA represent the amount Company A would charge if Makayla drives xx miles, and let BB represent the amount Company B would charge if Makayla drives xx miles. Write an equation for each situation, in terms of x, commax, and determine which company would be cheaper if Makayla needs to drive 35 miles with the rented truck.

Answer 1

Let's define the cost equations for each company based on the information given.

1. For Company A:

   • Initial fee: $95
   • Cost per mile: $1
   • Cost equation: \[ A(x) = 95 + 1x \] or \[ A(x) = 95 + x \]

2. For Company B:

   • Initial fee: $75
   • Cost per mile: $2
   • Cost equation: \[ B(x) = 75 + 2x \]

Now, if Makayla needs to drive 35 miles, we can substitute \( x = 35 \) into both equations to find the total costs.

For Company A: \[ A(35) = 95 + 1(35) = 95 + 35 = 130 \]

For Company B: \[ B(35) = 75 + 2(35) = 75 + 70 = 145 \]

Now, let's compare the costs:

• Company A's charge for driving 35 miles: $130
• Company B's charge for driving 35 miles: $145

Since $130 (Company A) is less than $145 (Company B), Company A would be the cheaper option for Makayla if she needs to drive 35 miles.