Quadratic equation

Question

Jackson and jane are saving up together to buy a car. After x weeks, jackson saces $(xsqaure +10) and jane saves $7x.

 

(a) how long will it take for jackson and jane to first save the same amount of money?

 

(B) if the cost of a 2nd hand car is $32 500, how long will it take for jackson and jane to save up that amount together?

Answer 1

Jackson = x² + 10

Jane = 7x

 

a)

 

Set the quadratic and linear equal to each other.

 

x² + 10 = 7x

 

 

Subtract 7x to both sides of equation.

 

x² - 7x + 10 = 0

 

 

Factor the left side.

 

(x - 2)(x - 5) = 0

 

x = 2     or       x = 5

 

 

Since the first point intersection occurs at x=2, it will take both of them 2 weeks to first save the same amount of money.