You have $5,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 15 percent and Stock Y with an expected return of 8 percent.
If your goal is to create a portfolio with an expected return of 10.5 percent, you will invest $___ in Stock X and $___ in Stock Y.

Explanation:

x = amount to invest in stock X

y = amount to invest in stock Y

x+y = 5000 = total amount to invest

y = 5000-x after subtracting x from both sides

If you invest x dollars and get a 15% return, then you earn 0.15x dollars

Let A = 0.15x

If you invest y = 5000-x dollars and get a 8% return, then you earn 0.08y = 0.08(5000-x) = 400-0.08x dollars in return

Let B = 400-0.08x

In total, you would earn A+B = 0.15x+(400-0.08x) = 0.07x+400 dollars. Set this equal to 10.5% of 5000, which is 0.105*5000 = 525. This means we want to earn 525 dollars in return. Set 0.07x+400 equal to 525 and solve for x

So,

0.07x+400 = 525

0.07x = 525-400

0.07x = 125

x = 125/0.07

x = 1785.71

y = 5000-x

y = 5000-1785.71

y = 3214.29