SOLUTION: Having trouble please help. I have to setup a system of equations (3 variables) needed to solve the problem below. Define each variable. Solve using the method of elimination. J

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Having trouble please help. I have to setup a system of equations (3 variables) needed to solve the problem below. Define each variable. Solve using the method of elimination. J      Log On


   

Question 106094: Having trouble please help.
I have to setup a system of equations (3 variables) needed to solve the problem below. Define each variable. Solve using the method of elimination. Just need help for the equations and i can solve from ther. thank you

a person takes three daily vitamins supplement,B,C and E, via three types of pills, regular, extra-strenght, and fortified. Each regular pills contains 10 units of B, 20 units of C, and 20 units of E. Each ectra-strenght pill contains 20 units of B, 60 units of C, and 10 units of B. Each fortified pill contains 10 units of B, 20 units of C, and 40 units of E. How many pills of each type should be in order to achieve 50units of B, 120 units of C, and 90 units of E?

Found 2 solutions by Fombitz, stanbon:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
R=10B%2B20C%2B20E
X=20B%2B60C%2B10E
F=10B%2B20C%2B40E
where R is regular pill, X is extra-strength pill, and F is fortified pills.
Let's say I take "m" R pills, "n" X pills, and "p" F pills to achieve 50 units of B, 120 units of C, and 90 units of E.
mR=10mB%2B20mC%2B20mE
nX=20nB%2B60nC%2B10nE
pF=10pB%2B20pC%2B40pE
mR%2BnX%2BpF=50B%2B120C%2B90E
Therefore equating units of B,C, and E,
10m%2B20n%2B10p=50
20m%2B60n%2B20p=120
20m%2B10n%2B40p=90
Good luck with the solution.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
a person takes three daily vitamins supplement,B,C and E, via three types of pills, regular, extra-strenght, and fortified.
Each regular pills contains 10 units of B, 20 units of C, and 20 units of E.
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Each extra-str pill contains 20 units of B, 60 units of C, and 10 units of E.
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Each fortified pill contains 10 units of B, 20 units of C, and 40 units of E.
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How many pills of each type should be in order to achieve 50units of B, 120 units of C, and 90 units of E?
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Let x,y,and z be the number of regular,extra-str. and fortified pills.
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B equation: 10x + 20y + 10z = 50
C equation: 20x + 60y + 20z = 120
E equation: 20x + 10y + 40z = 90
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I used a TI caluculator to get x = 2 ; y = 1, z = 1
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Cheers,
Stan H.