can you help me with my hw

Question

John and Sarah are each saving money for a car. The total amount of money John will save is represented by the function       f(x) = 60 +5x. The total amount of money Sarah will save is given by the function g(x)=x^2 +46. after how many weeks, x, will they have the same amount of money saved? explain how you arrived at your answer.

Answer 1

Chayil,

 

After the appropriate number of weeks (x), the money saved by both will be the same.  That means at that time the two functions will equal each other:

 

g(x) = f(x)

 

So:

 

x² + 46 = 60 + 5x

 

Rearranging terms:

 

x² - 5x - 14 = 0

 

This quadratic function has two factors:

 

(x - 7)(x + 2) = 0 (-7 * 2 = -14 and -7 + 2 = -5)

 

Then, either x - 7 = 0 or x - 2 = 0

 

x - 7 = 0 => x = 7

 

x + 2 = 0 => x = -2

 

x =7 weeks is correct since we can't have a negative number of weeks.

 

Hope this helps!