Michelle has half of her investments in stock paying a 6% dividend and the other half in a stock paying 10% interest. If her total annual interest is $680, how much does she have invested?

let each of her halves be x

.06x + .10x = 680
.16x = 680
x = 4250

so she invested twice that or 8500

Well, it seems like Michelle is quite the daredevil with her investments! Let's call the amount she has invested x dollars. Since Michelle has half of her investments in the 6% dividend stock, the amount invested in that stock would be x/2 dollars. Similarly, the amount invested in the 10% interest stock would also be x/2 dollars. Now, to calculate the interest earned from each investment, we can use the formula:

Interest = Principal × Rate

For the 6% dividend stock, the interest earned would be (x/2) × 6/100 = 3x/100 dollars.

For the 10% interest stock, the interest earned would be (x/2) × 10/100 = x/20 dollars.

Adding up these two interests gives us a total annual interest of (3x/100) + (x/20) = (23x/100) dollars.

We know that the total annual interest is $680, so we can set up an equation:

(23x/100) = 680

To solve for x, we can cross-multiply:

23x = 68000

Dividing both sides by 23, we find:

x = 68000/23

So, Michelle has a total investment of approximately $2,956.52.

Let's denote the amount of money Michelle has invested as "x". Since she has half of her investments in a stock paying a 6% dividend, the amount invested in that stock would be 0.5x. The other half of her investments, or 0.5x, is in a stock paying a 10% interest rate.

For the stock paying a 6% dividend, the annual interest earned would be 0.06 * 0.5x = 0.03x.
For the stock paying a 10% interest rate, the annual interest earned would be 0.10 * 0.5x = 0.05x.

The total annual interest earned is $680, so we can write the equation:

0.03x + 0.05x = 680

Combining like terms:

0.08x = 680

To find x, we can divide by 0.08:

x = 680 / 0.08

Calculating the value:

x = 8500

Therefore, Michelle has $8500 invested.

To find out how much Michelle has invested, we need to set up an equation based on the information given.

Let's assume Michelle has x dollars invested in each stock.

According to the problem, Michelle has half of her investments in stock paying a 6% dividend. This means she has 0.5x dollars invested in that stock.

Similarly, she has half of her investments in a stock paying a 10% interest, which means she also has 0.5x dollars invested in that stock.

Now, we can calculate the annual interest earned from each investment:

Annual interest from the 6% dividend stock = 0.5x * 0.06 = 0.03x dollars
Annual interest from the 10% interest stock = 0.5x * 0.10 = 0.05x dollars

According to the problem, the total annual interest earned is $680. So we can set up an equation combining the annual interest earned from both stocks:

0.03x + 0.05x = 680

Combining like terms, we get:

0.08x = 680

To solve for x, divide both sides of the equation by 0.08:

x = 680 / 0.08

x ≈ 8500

Therefore, Michelle has approximately $8,500 invested.