Question

Alonzo will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $50 and costs an additional 0.10 per mile driven. The second plan has no initial fee but costs 0.60 per mile driven. How many miles would Alonzo need to drive for the two plans to cost the same? Answers 1. Answer: 100 miles Step-by-step explanation: If Alonzo drives 0 miles, then the first plan would cost him 50 dollars and the second plan would cost him nothing. If Alonzo drives 10 miles, then the first plan would cost him 51 dollars and the second plan would cost him 6 dollars. From these statements, we can observe that the second plan is increasing at a rate 6 times the first one and will overtake it at one point. Our solution is the point of intersection between these two functions – where they cost the same. To find this, equate 0.1x + 50 = 0.6x where x is the number of miles Alonzo drives, multiply the equation with 10 to get, x + 500 = 6x subtract x, 5x = 500 and divide 5, x = 100. So at 100 miles, both plan 1 and 2 will cost 60$. This is our answer. Good Luck!