Question

Marge's income from two stocks each year totals $280. Stock A pays dividends at the rate of 5% and stock B at the rate of 6%. If she has invested a total of $5000, how much is invested in each stock?

Answer 1

To determine the amount invested in each stock, we can set up a system of equations. By solving the system of equations, we can find that Marge has invested $2000 in Stock A and $3000 in Stock B.

Step-by-step explanation:

To determine how much is invested in each stock, we can set up a system of equations based on the given information. Let's denote the amount invested in Stock A as 'x' and the amount invested in Stock B as 'y'. According to the problem, the total amount invested is $5000, so we have the equation x + y = 5000. Additionally, Marge's income from Stock A (5% dividend rate) and Stock B (6% dividend rate) totals $280, so we have the equation 0.05x + 0.06y = 280.

We can now solve this system of equations using substitution or elimination. By substituting x = 5000 - y into the second equation, we get 0.05(5000 - y) + 0.06y = 280. Simplifying the equation, we have 250 - 0.05y + 0.06y = 280. Combining like terms, we get 0.01y = 30. Solving for y, we find that y = 3000. Substituting this value of y back into the first equation, we can find the value of x. x + 3000 = 5000, so x = 2000.

Therefore, Marge has invested $2000 in Stock A and $3000 in Stock B.