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Question 54151: Melisa has saved a total of $30,000 and wants to invest in three different stocks: Pepsico, IBM, and Microsoft. She wants the Pepsico amount to be $1000 less than twice the IBM amount and the Microsoft amount to be $2000 more than the total in the other two stocks. How much should she invest in each stock.
Solve using linear equation, system of three variable. The variables will be x,y, and z. Solve for each.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Melisa has saved a total of $30,000 and wants to invest in three different stocks: Pepsico, IBM, and Microsoft. She wants the Pepsico amount to be $1000 less than twice the IBM amount and the Microsoft amount to be $2000 more than the total in the other two stocks. How much should she invest in each stock.
Solve using linear equation, system of three variable. The variables will be x,y, and z. Solve for each.
:
1st equation: total of 3 investments: x=Pep; y = IBM; z = Micro
:
x + y + z = 30000
:
write equation for the following statements, arrange in standard form:
"Pepsico amount to be $1000 less than twice the IBM amount"
x = 2y - 1000
x - 2y = -1000
:
"Microsoft amount to be $2000 more than the total in the other two stocks."
z = x + y + 2000
x + y - z = -2000
:
Three equations in standard form
x + y + z = 30000
x -2y + 0 = -1000
x + y - z = -2000
:
Taking the 1st and 3rd equations, you can eliminate x & y
x + y + z = 30000
x + y - z = -2000
------------------subtract
0 + 0 + 2z = 32000
z = 32000/2
z = 16000
:
Take the 1st and 2nd equations, substitute 16000 for z and you have:
x + y + 16000 = 30000
x + y = 30000 - 16000
x + y = 14000
:
x + y = 14000
x - 2y = -1000
-------------- Subtract, eliminate x
0 + 3y = 15000
y = 15000/3
y = 5000
:
I'll let you find out what x is.
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