# A total of $14,000 is invested in 3 accounts earning 3%, 4%, and 5% annual interest. The combined interest for one year is $539. If the amount invested at 5% is three times the amount at 4%, find the amount invested at 3%.

## If the amounts are x,y,z then we have

x+y+z = 14000

.03x + .04y + .05z = 539

z = 3y

Now just solve for x

## Let's assume the amount invested at 4% is x dollars. Therefore, the amount invested at 5% is 3x dollars.

The total amount invested in all three accounts is $14,000, so we can write the equation:

x + 3x + (x + 3x) = 14,000

Combining like terms, we can simplify the equation to:

8x = 14,000

To find the value of x, we need to isolate it. We can do this by dividing both sides of the equation by 8:

x = 14,000 / 8

x = 1,750

Now that we know the amount invested at 4% is $1,750, we can find the amount invested at 3%.

Let's assume the amount invested at 3% is y dollars.

To calculate the interest earned at 3%, we multiply the amount invested by the interest rate:

(1,750)(0.03) = 52.5

The combined interest for one year is $539, so we can write another equation:

52.5 + (1,750)(0.04) + (3)(1,750)(0.05) = 539

Simplifying the equation, we get:

52.5 + 70 + 262.5 = 539

Adding the terms on the left side, we find that:

385 = 539

This is not true, so our assumed value for the amount invested at 3% is incorrect.

To find the correct value for y, we need to re-assume the amount invested at 3% and repeat the calculations.

Let's assume the amount invested at 3% is z dollars.

To calculate the interest earned at 3%, we multiply the amount invested by the interest rate:

z * 0.03 = 52.5

Simplifying the equation, we find:

0.03z = 52.5

To isolate z, we divide both sides of the equation by 0.03:

z = 52.5 / 0.03

z ≈ 1750

Now, since this matches our assumption, we can conclude that the amount invested at 3% is approximately $1,750.

## To solve this problem, we can set up a system of equations based on the given information.

Let's say the amount invested at 3% is x dollars.

According to the given information, the amount invested at 4% is three times the amount invested at 3%, so it would be 3x dollars.

The amount invested at 5% is three times the amount invested at 4%, so it would be 3 * 3x = 9x dollars.

Now, let's calculate the interest earned from each account.

The interest earned from the account with 3% interest would be x * 0.03 = 0.03x dollars.

The interest earned from the account with 4% interest would be 3x * 0.04 = 0.12x dollars.

The interest earned from the account with 5% interest would be 9x * 0.05 = 0.45x dollars.

According to the problem, the combined interest from all three accounts is $539, so we can set up the equation:

0.03x + 0.12x + 0.45x = 539

Now, we can simplify and solve for x:

0.60x = 539

Dividing both sides of the equation by 0.60 gives:

x = 898.33

Therefore, the amount invested at 3% is $898.33.