To solve this word problem, you can set up a system of equations to represent the information given. Let’s assign variables to the amounts invested in each account.

Let x be the amount invested in the account that earned 12%.

Let y be the amount invested in the account that suffered a 4% loss.

From the problem, we know that the total amount invested is $35,000, so we can write the equation:

x + y = 35,000

We also know that the first account earned a rate of return of 12% and the second account suffered a 4% loss. The total amount gained after one year is $1,080.00, so we can write the equation:

0.12x – 0.04y = 1,080.00

Now we have a system of two equations:

x + y = 35,000

0.12x – 0.04y = 1,080.00

To solve this system, we can use the method of substitution or elimination. Let’s use the substitution method.

Solve equation 1 for x:

x = 35,000 – y

Substitute this expression for x in equation 2:

0.12(35,000 – y) – 0.04y = 1,080.00

Simplify and solve for y:

4,200 – 0.12y – 0.04y = 1,080.00

4,200 – 0.16y = 1,080.00

-0.16y = 1,080.00 – 4,200

-0.16y = -3,120.00

y = -3,120.00 / -0.16

y = 19,500.00

Now we know that the amount invested in the account that suffered a 4% loss is $19,500.00.

Substitute this value for y in equation 1 to find x:

x + 19,500.00 = 35,000.00

x = 35,000.00 – 19,500.00

x = 15,500.00

So, $15,500.00 was invested in the account that earned 12%, and $19,500.00 was invested in the account that suffered a 4% loss.

In summary, $15,500.00 was invested in the account that earned a 12% rate of return, and $19,500.00 was invested in the account that suffered a 4% loss.