Mr. Collins and Ms. LaPointe are saving money to buy a new motorcycle. The total amount of money Mr. Collins will save is given by the function p(x) = 62 + 5x. The total amount of money Ms. LaPointe will save is given by the function a(x) = x2 + 38. After how many months, x, will they have the same amount of money saved?

We have been given that Mr. Collins and Ms. LaPointe are saving money to buy a new motorcycle. The total amount of money Mr. Collins will save is given by the function . The total amount of money Ms. LaPointe will save is given by the function . We are asked to find number of months when they have the same amount of money saved.

To solve our given problem, we will equate both equations as:

Since time cannot be negative, therefore, after 8 months they will have the same amount of money saved.