Question

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.

Answer 1

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
Answer:
They will have the same amount of money saved after:
x = 7 weeks