Brain Teasers
Granola Bar Boxes
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?
How many boxes of each flavor did he buy?
Hint
Make a chart, and guess and check.Answer
Mr. Smith bought 4 boxes of almond chunky, 2 boxes of chewy chocolate chip, and 3 boxes of super special raisin nut granola bars.4*8+2*10+3*12=88.
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Comments
That was fun. I got it. Yay for me!
Nice and simple challenge, good job
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
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
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
where in reality, 0
Only S=3 will satisfy the third condition.
Therefore:
S=3
C=2
A=4
Therefore:
S=3
C=2
A=4
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.
The clue regarding the total number of boxes is not needed.
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