Question 9449
Let x = number of cars owned by David
{{{7*sqrt(x) }}} = number Mark owns.


Now, the quotient of 29150/181 is just blowing smoke on you.  That would be 150, and the square root of 9 (more smoke!!) is 3, so the total cars owned is 150*3 or 450


So, finally, here is the equation:
{{{x + 7 sqrt(x) = 450}}}


To solve a radical equation, which this is, you msut isolate the radical term by subtracting x from each side of the equation.

{{{7sqrt(x) = 450 - x }}}


Next, square both sides--that is,  square the entire sides:
{{{(7sqrt(x))^2 = (450 - x)^2}}}
{{{49x = 450^2 - 900x + x^2 }}}
{{{0 = x^2 - 900x + 202500}}}


The numbers here are so large, that you could hardly hope to begin to factor it, although I suspect it DOES factor.  You can use the quadratic formula to solve it, or use the pluggable solver by Igor Chudov, the owner of this website.  


I'll try the pluggable solver.  The graph is not important here, only the solution to the equation.



*[invoke quadratic "x", 1, -949, 202500]


Notice that the equation DOES factor, and the solutions are 625 and 324.  The 625 is more cars than the total, so it must be rejected.  That means that David has 324 cars, and Mark has 450 - x = 126 cars.


Good problem.  There must be an easier way to solve it.  Maybe someone will find it.


R^2 at SCC