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Granola Bar Boxes

Math brain teasers require computations to solve.

 Puzzle ID: #27938 Fun: (2.64) Difficulty: (1.7) Category: Math Submitted By: lips Corrected By: norcekri

Mr. Smith needs snacks for all the students going on a field trip. He bought 9 boxes of granola bars containing a total of 88 bars. He wanted variety, so he purchased 3 different flavors, which happened to come from 3 different companies. The almond chunky granola bars were packaged 8 to a box, the chewy chocolate chip bars came 10 to a box, and the super special raisin nut package contained 12 per box. He bought the most boxes of almond chunky, but had the most raisin nut bars.

How many boxes of each flavor did he buy?

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 WJSMama Jan 07, 2006 That was fun. I got it. Yay for me! bigSWAFF_69_ Jan 07, 2006 Nice and simple challenge, good job mr_brainiac Jan 29, 2006 Good puzzle, using as much logic as algebra to solve a "story problem". Not as easy as it first seemed, a bit of a good challenge jvs13 May 16, 2007 Let A = almond chunky C = chocolate chip S = super raisin Given: first: 8A + 10C + 12S = 88 second: A + C + S = 9 third: (A>C) and (A>C) By multiplying second equation by 8 and subtracting it to the first equation, C = 8- 2S where in reality, 0 jvs13 May 16, 2007 where in reality, 0 jvs13 May 16, 2007 Only S=3 will satisfy the third condition. Therefore: S=3 C=2 A=4 javaguru Feb 05, 2009 The ratio of almond to raisin boxes must exceed the ratio of the number in each box, which is 2::3. The least number of boxes this is possible with is 3::4. So I started knowing these were the minimum number of almond and raisin boxes which are 3x12=36 plus 4x8=32. It's pretty easy to see the only possibility to make 88 is to add two boxes of ten each. The clue regarding the total number of boxes is not needed.