### Brain Teasers

# A + B + C + D

A, B, C, and D are all positive whole numbers. If A is to 2 as B is to 3; B is to 6 as C is to 8; and C is to 9 as D is to 12, what is the SMALLEST possible value for the sum: A + B + C + D ?

### Hint

A/2 = B/3 or 3A = 2BB/6 = C/8 or 8B = 6C ;

C/9 = D/12 or 12C = 9D .

What's the smallest positive whole numbers that satisfies all three of the above equations?

### Answer

43A = 6 , B = 9 , C = 12 , and D = 16 .

So, A + B+ C + D = 43.

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