You inherit one hundred thousand dollars. You invest it all in three accounts for one year. The first account pays 4% compounded annually, the second account pays 3% compounded annually, and the third account pays 2% compounded annually. After one year, you earn $3,650 in interest. If you invest five times the money in the account that pays 4% compared to 3%, how much did you invest in the 4% account?

Let x = amount invested in the 1st account

y = amount invested in the 2nd account

z = amount invested in the 3rd account

Because the total investment is $100,000, therefore

x + y + z = 100,000 (1)

Interest earned in one year from the accounts is $3,650, therefore

0.04x + 0.03y + 0.02z = 3,650

or

4x + 3y + 2z = 365,000 (2)

Because x = 5y, therefore obtain these 2 equations:

5y + y + z = 100,000

or

6y + z = 100,000 (3)

4 * (5y) + 3y + 2z = 365,000

or

23y + 2z = 365,000 (4)

Substitute z=1000,000 - 6y from (3) into (4).

23y + 2 (100,000 - 6y) = 365,000

23y + 200,000 - 12y = 365,000

11y = 165,000

y = $15,000

Therefore

x = 5y = $75,000

z = 100,000 - 6y = $10,000

Answer:

The amounts invested are

1st account: $75,000

2nd account: $15,000

3rd account: $10,000