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# help with variables

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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
+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
+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