Four positive integers \( A,B,C\) and \(D\) have a sum of 36. If \(A+2 = B-2 = C \times 2 = D \div 2\), what is the value of the product \(A \times B \times C \times D\)?
+128406 A+ 2 = B -2 A + 2 = C * 2 A + 2 = D/2
A + 4 = B (A+ 2) / 2 = C 2(A + 2) = D
So
A + B + C + D = 36
A + (A + 4) + (A + 2) /2 + 2(A + 2) = 36 multiply through by 2
2A + 2(A + 4) + (A + 2) + 4(A +2) = 72
2A + 2A + 8 + A + 2 + 4A + 8 = 72
9A + 18 = 72
9A = 72 - 18
9A = 54
A = 6 B = 10 C = 4 D = 16
A*B*C*D = 6 (10) (4) (16) = 3840
