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Let a b c d and e be positive integers. The sum of the four numbers on each of the five segments connecting "points" of the star is 28. What is the value of the sum a+b+c+d+e?

May 26, 2020

#1
+25565
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Let a b c d and e be positive integers.

The sum of the four numbers on each of the five segments connecting "points" of the star is 28.

What is the value of the sum $$a+b+c+d+e$$?

I assume:

$$\begin{array}{|lrcll|} \hline (1): & e+4+b &=& 28 \\ (2): & a+5+c &=& 28 \\ (3): & b+6+d &=& 28 \\ (4): & c+7+e &=& 28 \\ (5): & d+8+a &=& 28 \\ \hline \text{sum}: & 2(a+b+c+d+e) + 4+5+6+7+8 &=& 5*28 \\ & 2(a+b+c+d+e) + 30 &=& 140 \\ & 2(a+b+c+d+e) &=& 110 \\ & \mathbf{a+b+c+d+e} &=& \mathbf{55 } \\ \hline \end{array}$$

May 26, 2020