Question 1032340
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.