Brian has half of his investments in stock paying a $10 \%$ dividend and the other half in a stock paying $14 \%$ interest. If his total annual interest is $\$ 780$, how much does he have invested?
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Final Answer: The total amount Brian has invested is \(\boxed{6500}\).
Step 1 ：Let's denote the total amount Brian has invested as x. Then, half of his investments would be 0.5x. The total annual interest from the 10% dividend stock would be 0.10 * 0.5x and from the 14% interest stock would be 0.14 * 0.5x. The sum of these two amounts is equal to $780.
Step 2 ：So, we have the equation: 0.10 * 0.5x + 0.14 * 0.5x = 780.
Step 3 ：We can solve this equation to find the value of x, which is the total amount Brian has invested.
Step 4 ：The solution to the equation is 6500. This means that Brian has $6500 invested in total.
Step 5 ：Final Answer: The total amount Brian has invested is \(\boxed{6500}\).
