Formulate a system of equations for the situation below and solve.

An investment club has$480,000earmarked for investment in stocks. To arrive at an acceptable overall level of risk, management is considering stocks that have been classified into three categories: high-risk, medium-risk, and low-risk. They estimate that high-risk stocks will have a rate of return of14%/year; medium-risk stocks,9%/year; and low-risk stocks,5%/year. Members of the club have also decided that they should invest twice as much in high-risk stocks as the other two categories combined. Determine how much the club should invest in each type of stock if the investment goal is to earn a return of$55,200/year on the total investment. (Assume that all the money available for investment is invested.)

a. Define the variables, using x, y and z, using precise/specific language.

b. Report the system of equations:

c. Solve the system using the substitution or elimination method. Show your work on the written work you turn in through Canvas. Report the solution:

high-risk stocks$

high-risk stocks$

low-risk stocks$

d. State your answer in a sentence with units.