Let's write a linear equation to represent both situations:
Situation A: Unlimited mileage
Pa = 40
Pa = Price of renting a car in A.
Situation B: Not unlimited mileage
Pb = 30 + 0.15x
Pb = Price of renting a car in B.
x = mile over 100.
If plan A saves Lia money:
[tex]30+0.15x>40[/tex]To find x, let's subtract 30 from both sides and then divide the sides by 0.15:
[tex]\begin{gathered} 30+0.15x-30>40-30 \\ 0.15x>10 \\ \frac{0.15}{0.15}x>\frac{10}{0.15} \\ x>66.7 \end{gathered}[/tex]Considering that x is the miles over 100, in order to save money, Lia has to travel 100 + 66.7 miles = 166.7 miles.
Answer: 166.7 miles.
