An investment adviser invested $14,000 in two accounts. One investment earned 5% annual simple interest, and the other investment earned 2.5% annual simple interest. The amount of interest earned for 1 year was $540. How much was invested in each account?

amount invested at 5% --- x

amount invested at 2.5% --- 14000-x

solve for x
.05x + .025(14000-x) = 540

Let's assign variables to the unknowns in the problem. Let "x" represent the amount of money invested at 5% and "y" represent the amount of money invested at 2.5%.

We know that the total amount invested is $14,000, so we have the equation:

x + y = 14,000 ----(Equation 1)

We also know that the interest earned after 1 year was $540, and we can use the formula for simple interest to set up another equation:

0.05x + 0.025y = 540 ----(Equation 2)

Now we can solve the system of equations to find the values of x and y.

To eliminate decimals, let's multiply both sides of Equation 2 by 100 to clear the decimal points:

5x + 2.5y = 54,000 ----(Equation 3)

Now we can solve the system of equations composed of Equation 1 and Equation 3. We'll use the method of substitution:

From Equation 1, we can rearrange it to express x in terms of y:

x = 14,000 - y

Substituting this value of x into Equation 3:

5(14,000 - y) + 2.5y = 54,000

70,000 - 5y + 2.5y = 54,000

-2.5y = 54,000 - 70,000

-2.5y = -16,000

Dividing both sides of the equation by -2.5:

y = -16,000 / -2.5

y = 6,400

Now substitute this value of y back into Equation 1 to solve for x:

x + 6,400 = 14,000

x = 14,000 - 6,400

x = 7,600

Therefore, the investment adviser invested $7,600 in the account that earned 5% interest and $6,400 in the account that earned 2.5% interest.

To solve this problem, we need to set up an algebraic equation based on the given information.

Let's say the amount invested at 5% interest is x dollars, and the amount invested at 2.5% interest is $14,000 - x dollars (since the total investment amount is $14,000).

The equation can be set up as follows:

0.05x + 0.025(14,000 - x) = 540

Let's simplify the equation:

0.05x + 0.025(14,000) - 0.025x = 540

0.05x + 350 - 0.025x = 540

0.025x + 350 = 540

Now, subtract 350 from both sides:

0.025x = 540 - 350

0.025x = 190

To isolate x, divide both sides by 0.025:

x = 190 / 0.025

x = 7600

So, $7,600 was invested at 5% interest.

To find the amount invested at 2.5% interest, subtract $7,600 from the total investment amount:

$14,000 - $7,600 = $6,400

Therefore, $6,400 was invested at 2.5% interest.

In summary, $7,600 was invested at 5% interest, and $6,400 was invested at 2.5% interest.