Question 1200997: 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, 7%/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 Theo, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! a = amount invested in 15% stocks.
b = amount invested in 10% stocks.
c = amount invested in 7% stocks.
a + b + c = 400,000
.15a + .10b + .07c = 40,000
c = a + b
replace c with a + b in the two equations to get:
a + b + a + b = 400,000
.15a + .10b + .07a + .07b = 40,000
combine like terms to get:
2a + 2b = 400,000
.22a + .17b = 40,000
multiply both sides of the first equation by .11 and leave the second equation as is to get:
.22a + .22b = 44,000
.22a + .17b = 40,000
subtract the second equation from the first to get:
.05b = 4,000
solve for b to get:
b = 80,000
in the equation of 2a + 2b = 400,000, replace b with 80,000 to get:
2a + 160,000 = 400,000
subtract 160,000 from both sides of the equation to get:
2a = 240,000
solve for a to get:
a = 120,000
since c = a + b, then c = 200,000
your solution should be:
a = 120,000
b = 80,000
c = 200,000
a + b + c = 400,000
.15a + .10b + .07c = 18,000 + 8,000 + 14,000 = 40,000.
the requirements of the problem have been satisfied.
your solutioon is that 120,000 is invested in 15% stocks and 80,000 is invested in 10% stocks and 200,000 is invested in 7% stocks.
Answer by MathTherapy(10549)  (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, 7%/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 number of high-risk, medium-risk, and low-risk stocks invested in, be H, M, and L, respectively
Then we get: 
L + L = 400,000 ----- Substituting L for H + M in eq (i)
2L = 400,000
Amount invested in low-risk stocks, or 
H + M = 200,000 --- Substituting 200,000 for L in eq (ii) ----- eq (iv)
.15H + .1M + .07(200,000) = 40,000 ---- Substituting 200,000 for L in eq (iii)
.15H + .1M + 14,000 = 40,000
.15H + .1M = 26,000 ---- eq (v)
.1H + .1M = 20,000 ---- Multiplying eq (iv) by .1 ------ eq (vi)
.05H = 6,000 ----- Subtracting eq (vi) from eq (v)
Amount invested in high-risk stocks, or 
120,000 + M = 200,000 ----- Substituting 120,000 for H in eq (iv)
Amount invested in medium-risk stocks, or 
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