Question

Lucy is deciding between two truck rental companies. Company A charges an initial fee of 65 for the rental plus1.50 per mile driven. Company B charges an initial fee of 30 for the rental plus2.50 per mile driven. Let AA represent the amount Company A would charge if Lucy drives X miles, and let BB represent the amount Company B would charge if Lucy drives X miles. Write an equation for each situation, in terms of X, comma X, and determine the number of miles driven, X, comma X, that would make the cost of each company the same.

Answer 1

Lucy can find the number of miles where the rental costs from Company A and Company B are the same by setting up equations for each company and equating them. Solving for X, it turns out that when Lucy drives 35 miles, the costs are equal.

Step-by-step explanation:

To determine the equation for each company's charges based on the number of miles driven, we can set up two equations where AA represents the cost for Company A and BB represents the cost for Company B. The equations are based on the provided charging schemes:

• For Company A: AA = 65 + 1.50X
• For Company B: BB = 30 + 2.50X

To find out for which number of miles driven (X) the cost of both companies would be the same, we set the two equations equal to each other:

65 + 1.50X = 30 + 2.50X

Solving for X, we subtract 1.50X from both sides:

65 = 30 + X

Next, we subtract 30 from both sides:

X = 35 miles

Therefore, if Lucy drives 35 miles, the cost for both Company A and Company B will be the same.