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Four positive integers A, B, C and D have a sum of 36. If A+2 = B-2 = C+2 = D-2, what is the value of the product ABCD?

 Oct 2, 2021
 #1
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A + B + C + D = 36

 

A + 2 = B - 2 = C x 2 = D ÷ 2

 

A = B - 4
B = 2C + 2

C = D ÷ 4

D = 2A + 4

 

Let's find A first.

 

D = 2A + 4

C = (2A + 4) ÷ 4

    = 0.5A + 1
B = A + 4 

A + B + C + D = 36

A + A + 4 + 0.5A + 1 + 2A + 4 = 36

4.5A + 9 = 36

4.5 A = 27

A = 6

Since A = 6, 
B = A + 4 

   = (6) + 4

   = 10

 

C = 0.5A + 1

    = 0.5(6) + 1

    = 3 + 1

    = 4

 

D = 2A + 4 

    = 2(6) + 4

    = 12 + 4

    = 16

 

Which means the product of the four, ABCD = 6 * 10 * 4 * 16 = 3840, which is your answer 

 Oct 2, 2021
 #2
avatar+35057 
+1

A = C     and  B = D

a+  a + b + b = 36

a+b =18  

a+2 = b-2  

then    a = 7 b = 11      c = 11   and d= 7

 

7 * 11*7*11 = 170

 Oct 2, 2021
 #3
avatar+35057 
+1

*** edit ***    ( the last line is incorrect ...I added instead of multiplying)

 

A = C     and  B = D

a+  a + b + b = 36

a+b =18  

a+2 = b-2  

then    a = 7 b = 11      c = 11   and d= 7

 

7 * 11*7*11 = 170

 

7 * 11 *7 * 11 = 5929

ElectricPavlov  Oct 2, 2021

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