+0

# dora

0
63
4
+355

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?

waffles  Oct 21, 2017

#3
+5227
+1

Here's another interpretation.

a + 1 + 4 + c  =  28       →       a + c  =  23

a + 3 + 5 + d  =  28       →       a + d  =  20

b + 4 + 2 + d  =  28       →       b + d  =  22

b + 1 + 3 + e  =  28       →       b + e  =  24

c + 2 + 5 + e  =  28       →       c + e  =  21      Add all five of these equations together to get...

2a + 2b + 2c + 2d + 2e  =  110      Divide through by  2 .

a + b + c + d + e  =  55

hectictar  Oct 22, 2017
Sort:

#1
+78579
+2

(b + e) + 4 + ( b + d) + 6 +  (a + c) + 5 + (a + d) + 8 + ( c + e) + 7  = 28

(b + e)  + ( b + d)  +  (a + c)  + (a + d)  + ( c + e) + 30  =  28

(b + e)  + ( b + d)  +  (a + c)  + (a + d)  + ( c + e) = -2

2 [ a + b + c + d + e]  =  -2          divide both sides by 2

a + b + c + d + e  =   -1

CPhill  Oct 21, 2017
#2
+355
0

I don't think that's correct

waffles  Oct 22, 2017
#3
+5227
+1

Here's another interpretation.

a + 1 + 4 + c  =  28       →       a + c  =  23

a + 3 + 5 + d  =  28       →       a + d  =  20

b + 4 + 2 + d  =  28       →       b + d  =  22

b + 1 + 3 + e  =  28       →       b + e  =  24

c + 2 + 5 + e  =  28       →       c + e  =  21      Add all five of these equations together to get...

2a + 2b + 2c + 2d + 2e  =  110      Divide through by  2 .

a + b + c + d + e  =  55

hectictar  Oct 22, 2017
#4
+78579
+1