Madam beautiful had a total of 20000 to invest. She decided to invest part at 3% and the rest at 2%. After one year she earned a total of 520. How much did she invest at each rate? Use cramers rule?

Let's assume Madam Beautiful invested x amount at 3% and (20000 - x) amount at 2%.

According to the given information, the interest earned from the 3% investment is 0.03x, and the interest earned from the 2% investment is 0.02(20000 - x).

The total interest earned is 520, so we can write the equation:

0.03x + 0.02(20000 - x) = 520

Simplifying the equation, we get:

0.03x + 400 - 0.02x = 520

Combining like terms, we have:

0.01x + 400 = 520

Subtracting 400 from both sides, we get:

0.01x = 120

Dividing both sides by 0.01, we find:

x = 12000

So, Madam Beautiful invested $12,000 at 3% and $8,000 (20000 - 12000) at 2%.