Nicole and adam are each saving money for a car. the total amount of money nicole will save is represented by the function f (x) = 36 + 4x . the total amount of money adam will save is given by the function g (x) = x2 + 15. after how many weeks, x, will they have the same amount of money saved? explain how you arrived at your answer.

For this case we have the following functions:
 f (x) = 36 + 4x
 g (x) = x2 + 15
 By matching both functions we have:
 f (x) = g (x)
 36 + 4x = x2 + 15
 Rewriting we have:
 x2 + 15 - 4x - 36 = 0
 x2 - 4x - 21 = 0
 Solving the polynomial we have:
 (x-7) (x + 3) = 0
 x = -3
 x = 7
 Taking the positive root we have:
 x = 7
 
 They will have the same amount of money saved after:
 x = 7 weeks