Kate has a utility function

U(x,y) = 10x + y

The price of good x is $5,

and the price of good y is $20.

If Kate's income is $500, how

many units of good x would she

consume if she chose the bundle

that maximizes her utility subject

to her budget constraint?

Also, why does it become U(x,y)= 10x^1/2+10y?