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## A + B + C + D

Math brain teasers require computations to solve.

 Puzzle ID: #13954 Fun: (2.51) Difficulty: (2.15) Category: Math Submitted By: mathemagician

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 = 2B

B/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?

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 jacintan Jul 28, 2003 I didn't quite get that one........... luvupurple Jul 28, 2003 Why cann't A=2 B=3 C=4 D=5? Then 2+3+4+5=14. I didn't get it either. jimbo Jul 29, 2003 Nice one! Taking D to be 1... C is 3/4. B is 3/4 of C = 9/16 and A is 2/3 of B = 3/8. Since they must all be whole numbers, multiply everything by 16 (the LCM of the denominators). I like it! avril_lavigne Aug 02, 2003 ok.. now some just explain it in english please xiaobaby Aug 27, 2003 use ratio. A:B=2:3 A:B:C=4:6:8 C=9:12=3:4 A:B:C=12:18:24:32=6:9:12:16 heyevpos Jan 12, 2004 Thank you - very nice. javaguru Feb 10, 2009 Serious issue with the wording. You didn't specify that all the relationships had to be ratios. My answer was 0 + 1 + 3+ 4 = 7 A+2 = 2 B+2 = 3 B+5 = 6 C+5 = 8 C = 3/9 D = 3/12