Question 1183956: If 4M+N=20 and N+P=20, what is the value of M?
A.0
B.4
C.16
D.24
E.It cannot be determined from the information given.
The correct answer was E but I don't know how so can you explain? Thank you.
Found 2 solutions by ankor@dixie-net.com, ikleyn:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! If 4M+N=20 and N+P=20, what is the value of M?
try this
4M + N + __ = 20
__ + N + P = 20
---------------------subtraction eliminates N
4M - P = 0
P = 4M
:
Replace P with 4M in the second equation
N + 4M = 20
which is essentially the same as the 1st equation, so unable to go further
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! If 4M+N=20 and N+P=20, what is the value of M?
A.0
B.4
C.16
D.24
E.It cannot be determined from the information given.
The correct answer was E but I don't know how so can you explain? Thank you.
~~~~~~~~~~~~~~~~
You are given 2 equations for 3 variables
4M + N = 20 (1)
N + P = 20 (2)
From the second equation, express N = 20-P and substitute it into equation (1), replacing N there. You will get
4M + (20-P) = 20,
or
4M = P.
So, M may have ANY VALUE, depending on the value of P, which is not given.
THEREFORE, the answer to the problem question is option E. ANSWER
Notice that you have only two linear equations for three unknowns.
At these conditions, the system is underdetermined and have MANY solutions (more than one).
It explains the situation from the general point of view.
Completed.
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