Question:
Two truck rental companies have different rates. V-Haul has a base charge of $70.00, plus $0.50 per mile. W-Haul has a base charge of $65.60. plus $0.55 per mile. For how many miles would these two companies charge the same amount?
Solution:
First, denote by m the miles. Now, If V-Haul has a base charge of $70.00, plus $0.50 per mile, then the linear equation that describes this situation is:
[tex]70+\text{ 0.50m}[/tex]On the other hand, if W-Haul has a base charge of $65.60. plus $0.55 per mile, then the linear equation that describes this situation is:
[tex]65.60+\text{ 0.55m}[/tex]now, these companies charge the same amount when:
[tex]70+\text{ 0.50m = 65.60 + 0.55m}[/tex]this is equivalent to:
[tex]0.55m\text{ -0.50m = 70-65.60}[/tex]this is equivalent to:
[tex]0.05m\text{ = 4.4}[/tex]then, solving for m, we get:
[tex]m\text{ = }\frac{4.4}{0.05}\text{ = 88 miles }[/tex]then, we can conclude that the correct answer is:
if a driver drives 88 miles, those two companies would charge the same amount of money.
