Question

Juan invested $24,000 into two stocks. The first stock paid a 4% dividend, and the second stock paid a 3% dividend. If he received $800 in dividends in the first year, how much did he invest in each stock?

A) $12,000 in the first stock, $12,000 in the second stock
B) $16,000 in the first stock, $8,000 in the second stock
C) $8,000 in the first stock, $16,000 in the second stock
D) $18,000 in the first stock, $6,000 in the second stock

Answer 1

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.