<PRE><B>Question 1179825</B>
x + y + z = 500,000
x = high risk investment
y = medium risk investment
z = low risk investment


high risk gets 15%
medium risk gets 10%
low risk gets 6%


low risk investment equals sum of the other two investments.
z = x + y


goal is to get a return of 50,000 on the total investment.
.15x + .10y + .06z = 50,000


your two equations that need to be solved simultaneously are:


x + y + z = 500,000
.15x + .10y + .06z = 50,000


since z = x + y, then replace z with x + y in both equations to get:


x + y + x + y = 500,000
.15x + .10y + .06 * (x + y) = 50,000


combine like terms in the first equation and simplify the second equation to get:


2x + 2y = 500,000
.15x + .10y + .06x + .06y = 50,000


leave the first equation as is and combine like terms in the second equation to get:


2x + 2y = 500,000
.21x + .16y = 50,000


multiply both sides of the first equation by .08 and leave the second equation as is to get:


.16x + .16y = 40,000
.21x + .16y = 50,000


subtract the first equation from the second to get:


.05x = 10,000


solve for x to get:
x = 10,000 / .05 = 200,000


replace x with 200,000 in the first equation to get:
.16x + .16y = 40,000 becomes:
.16 * 200,000 + .16 * y = 40,000
simplify to get:
32000 + .16 * y = 40,000
subtract 32000 from both sides to get:
.16 * y = 8000
solve for y to get:
y = 8000 / .16 = 50,000


you have:


x = 200,000
y = 50,000


go back to your original equations and replace x and y with their respective values to get:


x + y + z = 500,000 becomes 200,000 + 50,000 + z = 500,000 which becomes 250,000 + z = 500,000.
solve for z to get:
z = 250,000


.15x + .10y + .06z = 50,000 becomes .15 * 200,000 + .10 * 50,000 + .06 * z = 50,000 which becomes 30,000 + 5,000 + .06 * z = 50,000 which becomes 35000 + .06 * z = 50,000.
subtract 35,000 from both sides to get:
.06 * z = 50,000 - 35,000 = 15,000.
solve for z to get:
z = 15,000 / .06 = 250,000


you now have;


x = 200,000
y = 50,000
z = 250,000
.15 * x = 30,000
.10 * y = 5,000
.06 * z = 15,000


z = x + y so that part is good.
your solution is:
amount invested in high risk is 200,000.
amount invested in medium risk is 50,000
amount invested in low risk is 250,000









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