Final answer:
By setting up a system of equations with x and y representing the amounts invested in the first and second stocks, and solving for both variables, we find that Juan invested $8,000 in the first stock and $16,000 in the second stock.
Step-by-step explanation:
To solve this problem, we can set up a system of equations based on the total amount invested and the dividend payments received. Let's denote the amount invested in the first stock as x and the amount invested in the second stock as y. We know that the total investment is $24,000 and the total dividends received is $800. Therefore, we can represent the investments and the dividends with the following equations:
- x + y = $24,000 (Total investment)
- 0.04x + 0.03y = $800 (Total dividends)
Next, we solve the system using substitution or elimination. In this case, let's use the substitution method to find the values of x and y. We can express y in terms of x from the first equation as follows:y = $24,000 - x
Now, substitute this expression for y in the second equation:
0.04x + 0.03($24,000 - x) = $800
0.04x + $720 - 0.03x = $800
0.01x = $80
x = $8,000Therefore, the first stock has an investment of $8,000. To find the investment in the second stock, we use the expression for y:
y = $24,000 - $8,000
y = $16,000
Juan invested $8,000 in the first stock and $16,000 in the second stock, which corresponds to option C.