Equations for F

Given that
A + B = C
C + D = E
E + A = F
B + D + F = 100
A = 8
What is the value of F?
Source: mathcontest.olemiss.edu 3/3/2008

SOLUTION
Let’s label these five equations for ease in reference as follows:
A+B=C        (1)
C+D=E        (2)
E+A=F        (3)
B+D+F=100        (4)
A=8             (5)

Rewrite Eq. (3) and add it to Eq. (4):
E+A-F=0
B+D+F=100
————————-
E+A+B+D=100        (6)

Rewrite Eq. (1) and Eq. (2) and add them:
A+B-C=0
C+D-E=0
———————
A+B+D-E=0        (7)

Multiply Eq. (7) by -1 and add it to Eq. (6):
E+A+B+D=100
-A-B-D+E=0
—————————–
2E=100
E=100\div 2=50

Value of F
Substitute the values of A,E into Eq. (3):
E+A=F
50+8=F
58=F

Answer: 58.

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About mvtrinh

Retired high school math teacher.
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