A woman has $500,000 invested in two rental properties. One yields an annual return of 10% on her investment, and the other returns 12% per year on her investment. Her total annual return from the two investments is $53,000. Let x represent the amount of the 10% investment and y represent the amount of the 12% investment.

(a) Write an equation that states that the sum of the investments is $500,000.

(b) What is the annual return on the 10% investment?

(c) What is the annual return on the 12% investment?

(d) Write an equation that states that the sum of the annual returns is $53,000.

(e) Solve these two equations simultaneously to find how much is invested in each property?