Katie invested a total of ​$6000

​,
part at 3
​%
simple interest and part at 4
​%
simple interest. At the end of 1​ year, the investments had earned ​$214

interest. How much was invested at each​ rate?

Good subject

Let's assume Katie invested x dollars at 3% simple interest.

This means she invested (6000 - x) dollars at 4% simple interest.

The interest earned from the 3% investment can be calculated as:

Interest_3% = x * 0.03

The interest earned from the 4% investment can be calculated as:

Interest_4% = (6000 - x) * 0.04

The total interest earned is given as $214, so we can write the equation:

Interest_3% + Interest_4% = $214

Substituting the equations for the interest earned:

x * 0.03 + (6000 - x) * 0.04 = $214

Simplifying the equation:

0.03x + 240 - 0.04x = $214

Combining like terms:

-0.01x = $214 - $240

Simplifying further:

-0.01x = -$26

To solve for x, we divide both sides of the equation by -0.01:

x = -$26 / -0.01

x = $2600

Therefore, Katie invested $2600 at 3% simple interest and (6000 - 2600) = $3400 at 4% simple interest.

To solve this problem, let's assume that Katie invested some amount, x, at 3% interest, and the remaining amount, 6000 - x, at 4% interest.

The interest earned from the investment at 3% interest is given by the formula: interest = principal * rate * time. So, the interest earned at 3% interest is 0.03x.

Similarly, the interest earned from the investment at 4% interest is given by the formula: interest = principal * rate * time. So, the interest earned at 4% interest is 0.04(6000 - x).

We are given that at the end of 1 year, the investments had earned $214 in interest. So, we can write the equation:

0.03x + 0.04(6000 - x) = 214

Now, let's solve this equation to find the value of x:

0.03x + 0.04(6000 - x) = 214
0.03x + 240 - 0.04x = 214
-0.01x = -26
x = -26 / -0.01
x = 2600

Now that we have found x, we can determine the amount invested at each rate:

Amount invested at 3% interest = $2600
Amount invested at 4% interest = $6000 - $2600 = $3400

So, Katie invested $2600 at 3% interest and $3400 at 4% interest.

amount invested at 3% --- x

amount invested at 4% --- 6000-x

.03x + .04(6000-x) = 214

continue...