Formulate but do not solve the problem.
A private investment club has $600,000 earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high-risk, medium-risk, and low risk. Management estimates that high-risk stocks will have a rate of return of 15%/year; medium-risk stocks, 12%/year; and low risk stocks, 5%/year. The members have decides that the investment in medium-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $60,000/year on the total investment. (Assume that all the money available for investment is invested). Let x be the amount of money invested in high-risk stocks, y be the amount of money invested in medium-risk stocks, and z be the amount of money invested in low-risk stocks.

Question

Formulate but do not solve the problem. ​
A private investment club has $600,000 earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high-risk, medium-risk, and low risk. Management estimates that high-risk stocks will have a rate of return of 15%/year; medium-risk stocks, 12%/year; and low risk stocks, 5%/year. The members have decides that the investment in medium-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $60,000/year on the total investment. (Assume that all the money available for investment is invested). Let x be the amount of money invested in high-risk stocks, y be the amount of money invested in medium-risk stocks, and z be the amount of money invested in low-risk stocks.
​

Quizplus · Accepted Answer

Since the investment in medium-risk stocks should be equal to the sum of the investments in the other two categories, we can say that:

y = x + z

Also, we can set up an equation for the total return on investment:

0.15x + 0.12y + 0.05z = 60,000

Substituting the value of y from the first equation into the second equation, we get:

0.15x + 0.12(x + z) + 0.05z = 60,000

Simplifying and rearranging, we get:

0.27x + 0.17z = 60,000

Using the fact that all the money available is invested, we can say that:

x + y + z = 600,000

Substituting the value of y from the first equation into this equation, we get:

x + x + z + z = 600,000

Simplifying, we get:

2x + 2z = 600,000

x + z = 300,000

Now we have two equations:

0.27x + 0.17z = 60,000 
x + z = 300,000

Solving these equations gives:

x = $225,000 invested in high-risk stocks 
y = $150,000 invested in medium-risk stocks 
z = $225,000 invested in low-risk stocks

Therefore, the best choice is B.

Formulate but Do Not Solve the Problem. ​

Formulate but Do Not Solve the Problem.