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On a box of granola bars it says: "60 % bigger than regular granola bar (based on weight compared to regular bar").

The regular, 24 g, granola bars come in a box of 8 bars.

The big, 42 g, granola bars come in a box of 5 bars.

Now obviously 42 is 75 % bigger than 24.

Why is the claim that the big bar is 60 % bigger than the regular bar actually correct?

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closed as off-topic by Gareth McCaughan, boboquack, Rand al'Thor, Rubio, Beastly Gerbil Mar 20 '17 at 7:04

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    $\begingroup$ 42 is NOT 75 % bigger than 24 $\endgroup$ – newzad Jun 11 '16 at 20:20
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    $\begingroup$ @nikamed: 24 + 50 % (12) = 36, 24 + 100 % (24) = 48, 24 + 75 % (18) = 42 $\endgroup$ – granola Jun 11 '16 at 20:31
  • $\begingroup$ Already tried: 192/210, 3/8.4 don't work $\endgroup$ – ev3commander Jun 12 '16 at 1:11
  • $\begingroup$ Is this something you came up with, or does it come from an actual box of granola bars? (If it's from a real box, you could add the real tag.) $\endgroup$ – f'' Jun 12 '16 at 3:26
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    $\begingroup$ How is the claim "actually correct"? The accepted answer provides a way to arrive at the calculation the claim uses, but the claim is clearly incorrect given its wording. $\endgroup$ – KeyboardWielder Jun 12 '16 at 18:09
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The only thing that makes sense given the information in the question is that it takes up 60% more of the proportional of total weight in the package — that is, 1/5 of the box is 60% more than 1/8 of the box.

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  • $\begingroup$ That's the only number that's 60% larger than another number in the question's information, so I came up with that. $\endgroup$ – Joe Z. Jun 12 '16 at 1:33
  • $\begingroup$ I think you're on the right track. $\endgroup$ – granola Jun 12 '16 at 1:53
  • $\begingroup$ Can you give a hint as to where to go from there? $\endgroup$ – Joe Z. Jun 12 '16 at 2:10
  • $\begingroup$ Do you have a calculation which results in 60 %? $\endgroup$ – granola Jun 12 '16 at 2:14
  • $\begingroup$ Start with the calculation which produces 75 % and modify it to get 60 %. $\endgroup$ – granola Jun 12 '16 at 2:25
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Use the Geometric Mean of the two quantities.

This is the standard for reporting percentage changes in accounting, so it's not entirely without precedent. The geometric mean of 24 and 42 is 31.7.
24 is .755*31.7, 42 is 1.32*31.7. The difference between the two coefficients is .57, (or 57%), which is close to 60%.

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Let me preface the answer by saying I'm not a professional mathematician or skilled puzzlist. In anyone wishes to correct my explanation please feel free to do so.

There are 2 calculations involved.

First how much bigger is the big bar compared to the regular bar?

(42 g - 24 g) is what per cent of 24 g?

(42 g - 24 g) = x % * 24 g

18 g      =  x % * 24 g

18 g / 24 g = x %

0.75 = x %

0.75 * 100 = x * 100

   75 %   =  x

The big bar is 75 % bigger than the regular bar. Note that this is individually -- 1 big bar is 75 % bigger than 1 regular bar.

Yet the box says the big bar is 60 % bigger than the regular bar by weight.

The 60 % figure must refer to the difference between a bar from a entire box of each size of bar.

There are 8 bars in the regular size box: 8 * 24 g = 192 g.

There are 5 bars in the big size box: 5 * 42 g = 210 g.

The big size box has 210 g - 192 g = 18 g more product. These 18 g are distributed over 5 bars (18 g / 5 bars = 3.6 g per bar).

Secondly how much bigger is the big bar compared to the regular bar taking into account an entire box of 5 big bars versus an entire box of 8 regular bars? Subtract out 3.6 g from the big bar.

((42 g - 3.6 g) - 24 g) is what per cent of 24 g?

(38.4 g - 24 g) = x % * 24 g

14.4 g      =  x % * 24 g

14.4 g / 24 g = x %

0.6 = x %

0.6 * 100 = x * 100

   60 %     =  x

The 60 % value is a comparison between an entire box of bars and not between individual bars.

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  • $\begingroup$ That does effectively the same thing as my answer — normalize the weights over the weight of a whole box. $\endgroup$ – Joe Z. Jun 12 '16 at 3:09

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