|
Question 1032340: john and sarah are saving money for a car. the total amount of money john will save is given by the function f(x)=60+50x. the total amount of money sarah would save is given by the function g(x)= x squared + 46. after how many weeks, x, will they have the same amount of money saved? explain how you arrived at your answer.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! f(x) = 60 + 50 * x
g(x) = x^2 + 46
f(x) is the amount of money that john saved.
g(x) is the amount of money that sarah saved.
they will have saved the same money when g(x) = f(x)
if you subtract f(x) from both sides of the equation, you get:
g(x) - f(x) = 0
since g(x) = x^2 + 46 and f(x) = 60 + 50x, then g(x) - f(x) becomes:
x^2 + 46 - 60 - 50x = 0
combine like terms to get:
x^2 - 50x - 14 = 0
if you factor this quadratic equation, you will get:
x = -.278 or x = 50.278
x can't be negative, so x has to be 50.278 weeks.
when x = 50.278 weeks, you get:
f(x) = 60 + 50x = 60 + 50 * 50.278 = 2573.9
g(x) = x^2 + 46 = (50.278)^2 + 46 = 2573.877284 which rounds to 2573.9.
the difference between the two is in the rounding.
|
|
|
| |
