SOLUTION: ----------- ----------- ----------- -- || _ || 7 || _ || _ || _ || 10 || _ || ----------- ----------- ----------- -- If in each box of the previous diagram a number is placed,

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Question 1197421: --------------------------------------
|| _ || 7 || _ || _ || _ || 10 || _ ||
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If in each box of the previous diagram a number is placed, not necessarily different from the others, so that the sum of the numbers in any of three consecutive boxes is 25, what number goes in the fourth box?
A) 7
B) 8
C) 10
D) 17
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
--------------------------------------------
||  A ||  7 ||  B ||  C ||  D || 10 ||  E ||
--------------------------------------------

system%28A%2B7%2BB=25%2C7%2BB%2BC=25%2C+B%2BC%2BD=25%2C+C%2BD%2B10=25%2C+D%2B10%2BE=25%29

system%28A%2BB=18%2CB%2BC=18%2C+B%2BC%2BD=25%2C+C%2BD=15%2C+D%2BE=15%29

A+B = B+C = 18, so
  A = C

C+D = D+E = 15, so
  C = E, so

A = C = E

Substituting C for A and E

system%28C%2BB=18%2CB%2BC=18%2C+B%2BC%2BD=25%2C+C%2BD=15%2C+D%2BC=15%29

Eliminating equivalent equations:

system%28B%2BC=18%2C+B%2BC%2BD=25%2C+C%2BD=15%29

Subtracting the 1st equation from the 2nd

B+C+D=25
B+C  =18
--------
    D=7

 C+D=15
 C+7=15
   C=8, and since  A = C = E, A=8, E=8

and since B+C=18
          B+8=18
            B=10

So the solution is

--------------------------------------------
||  A ||  7 ||  B ||  C ||  D || 10 ||  E ||
--------------------------------------------

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|| __ ||  7 || __ || __ || __ || 10 || __ ||
--------------------------------------------

--------------------------------------------
||  8 ||  7 || 10 ||  8 ||  7 || 10 ||  8 ||
--------------------------------------------
Edwin

Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


--------------------------------------
|| _ || 7 || _ || _ || _ || 10 || _ ||
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Let x be the number in the first box.

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|| x || 7 || _ || _ || _ || 10 || _ ||
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The sum of the numbers in boxes 1 to 3 is 25, so the number in box 3 is 18-x.

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|| x || 7 || 18-x || _ || _ || 10 || _ ||
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The sum of the numbers in boxes 2 to 4 is 25, so the number in box 4 is x.

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|| x || 7 || 18-x || x || _ || 10 || _ ||
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The sum of the numbers in boxes 3 to 5 is 25, so the number in box 5 is 7.

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|| x || 7 || 18-x || x || 7 || 10 || _ ||
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The sum of the numbers in boxes 4 to 6 is 25, so the number in box 4 is 8.

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|| x || 7 || 18-x || 8 || 7 || 10 || _ ||
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ANSWER: 8