Bob won a $200,000 lottery. He invests part of the money in real estate with an annual return of 3% and the rest in a money market account at 4.5% interest. If the annual interest on the money was $8250, how much was invested at each rate?

Bob invested $50,000 in real state and $150,000 in a money market.

Step-by-step explanation:

Assuming that x is the investment in real state:

(200,000-x) * 0.045 + x * 0.03 = 8,250

Apply distributive property:

(200,000*0,045) - 0.045x + 0.03x = 8,250

9,000 - 0.045x + 0.03x = 8,250

We must clear x:

- 0.045x + 0.03x = 8,250 - 9,000

-0.015x = - 750

x = - 750/-0.015

x = 50,000

So, the invest in real state is $50,000.

$200,000 - $50,000 = $150,000 is the invest in a money market.