I found width=13.72 ft and length=43.72 ft.
Call one dimension of the rectangle x, the other will be x+30
You want an area A=600 ft^2 but A=length x width=x*(x+30)=600
Rearranging you get:

solving this quadratic equation you get a negative solution and a positive one that gives your result.
The bike will cost $481.50
because
10% off of 500 is 50
so 500 - 50 = 450
Now include the sales tax which is
450 * 0.07 = 31.5
Now add the two totals to get
$481.50
Negative Exponent Rule:
this says that negative exponents in the numerator get moved to the denominator and become positive exponents. Negative exponents in the denominator get moved to the numerator and become positive exponents.
Like this||
If H represents the tome teams tickets and V represents the visiting teams then it would be v+h(5)=52,000.
V= 8,667 tickets
H= 43,333 tickets