Question 1201131: Formulate a system of equations for the situation below and solve.
A private investment club has $400,000 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, 10%/year; and low-risk stocks, 6%/year. The members have decided that the investment in low-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 $40,000/year on the total investment. (Assume that all the money available for investment is invested.)
high-risk stocks $
medium-risk stocks $
low-risk stocks $
Found 2 solutions by mananth, MathTherapy:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! high-risk stocks $ amount invested be z ----15%
medium-risk stocks $ amount invested be y-----10%
low-risk stocks $ amount invested be x-------6%
Total investment $400,000
Condition
x = y+z...................(1)
x+y+z =400000..............(2)
6%x+10%y+15%z =40,000..........(3)
x+y+z =400000 (x=y+z)
x+x = 400000
x=200000
Therefore y+z =200 000....................(4)
6%x+10%y+15%z =40,000 multiply by 100
6x+10y+15z =4000000
6(y+z)+10y+15z = 4000000
16y+21z = 4000000................(5)
Solv (4) &(5)
5z =800000
z= 160000
y= 200000-160000 =40000
high-risk stocks $ amount invested 160,000
medium-risk stocks $ amount invested 40,000
low-risk stocks $ amount invested 200,000
Answer by MathTherapy(10551)  (Show Source):
You can put this solution on YOUR website!
Formulate a system of equations for the situation below and solve.
A private investment club has $400,000 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, 10%/year; and low-risk stocks, 6%/year. The members have decided that the investment in low-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 $40,000/year on the total investment. (Assume that all the money available for investment is invested.)
high-risk stocks $
medium-risk stocks $
low-risk stocks $
Let high, medium, and low-risk amounts be H, M, and L, respectively. We then get the following equations:
H + M + L = 400,000 -- eq (i)
L = H + M____H + M - L = 0 -------- eq (ii)
.15H + .1M + .06L = 40,000 --- eq (iii)
2L = 400,000 ---- Subtracting eq (ii) from eq (i)
Amount invested in the low-risk stocks, or 
H + M = 200,000 ---- Substituting 200,000 for L in eq (ii)
M = 200,000 - H ----- eq (iv)
.15H + .1(200,000 - H) + .06(200,000) = 40,000 ----- Substituting 200,000 - H for M, and 200,000 for L, in eq (iii)
.15H + 20,000 - .1H + 12,000 = 40,000
.15H - .1H = 40,000 - 32,000
.05H = 8,000
Amount invested in the high-risk stocks, or 
You should now be able to determine the amount invested in the medium-risk by substituting 160,000 for H in eq (iv)
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