Thread: System of Equations/Logic Puzzle Help

Solve for a+b+c+d+e.

a+b=10
b+c=-7
c+d=3
d+e=11
e+a=1

Hello, Espionage!

$\displaystyle \text{Solve for }a+b+c+d+e.$

. . $\displaystyle \begin{array}{ccc}a+b&=& 10 \\ b+c&=&\text{-}7 \\ c+d&=&3 \\ d+e&=&11 \\ e+a&=&1\end{array}$

Add the equations:

. . $\displaystyle (a + b)+(b+c)+(c+d)+(d+e)+(e+a) \;=\;10 - 7 + 3 + 11 + 1$

. . $\displaystyle 2a + 2b + 2c + 2d + 2e \;=\;18$

. . . . . . $\displaystyle a+b+c+d+e \;=\;9$

Originally Posted by Soroban

Hello, Espionage!


Add the equations:

. . $\displaystyle (a + b)+(b+c)+(c+d)+(d+e)+(e+a) \;=\;10 - 7 + 3 + 11 + 1$

. . $\displaystyle 2a + 2b + 2c + 2d + 2e \;=\;18$

. . . . . . $\displaystyle a+b+c+d+e \;=\;9$

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