Math Is Fun Forum

Joseph

Guest

6 grade math

If a 27 in. to the third power jar of peanut butter holds 16 ounces, how much peanut butter is in a jar that is 67.5 in. to the third power in volume.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: 6 grade math

A 3 by 3 by 3 inch cube is the first one, or 16 ounces.
Now 5 + 6 + 7 is like 6 + 6 + 6, so it is divisible by 3, just for interest or fun.
So to visualize an shape, let me fiddle with numbers.
67.5 is 3 by X by Y.     X times Y = 22.5 or at least this is one possibility.
There are other shapes don't forget though...
I just learned that 13.5 is 60% of 22.5 so I'll use that.
Now the big shape called 67.5 could be
many shapes, but one shape is a
rectangular cube with these sizes:  3 high by 1/0.6 wide by 13.5 deep.
See how the 3 directions multiply to 67.5.
Are you confused by the 1 over 0.6 ??  1/0.6 ??
This is about 1.62 or something.  (Woops: 1.666666, should have known due to 100/6)
Actually, off the subject 1/1.618034 is close to 0.618034: the golden ratio.
But now back to the answer.
If 16 ounces is 3 by 3 by 3,
and then how many ounces is 3 by 22.5 by 1 ??
Well 3 by 3 is 9 and
22.5 by 1 is 22.5
22.5 is bigger than 9.
And the ounces answer will be bigger than 16 then.
9 + 9 is 18 and 4.5 more is 22.5
4.5 is half of 9.
So 2 and a half times 9 is 22.5
So the volume of 16 ounces times 2 and a half is the answer.
16 + 16 + 8 = 40 ounces is the answer.

Last edited by John E. Franklin (2008-01-25 14:35:36)

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igloo myrtilles fourmis

Joseph

Guest

Re: 6 grade math

can u sum that up?

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: 6 grade math

A faster way to do this is like this.
Do two things at the same time.
Whatever you do to the 27 volume,
you also do to the 16 ounces.
So 27 + 27 + 27/2 = 54 + 13 1/2 = 67 1/2 = big volume
So 16 + 16 + 16/2 = 32 + 8 = 40 ounces = answer for big volume.

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igloo myrtilles fourmis

TheDude

Member

Registered: 2007-10-23

Posts: 361

Re: 6 grade math

First of all, Joseph, we're working with volume here.  In that case you would say that the first container is 27 cubic inches, not 27 inches to the third power.  If it's a unit of measurement that's being raised to a power then it represents another unit, like square inches represent area, cubic inches represent volume, etc.

Secondly, I would just use ratios for this.  Your 27 cubic inch container holds 16 oz. of peanut butter, and you want to know how much peanut butter can be held in a 67.5 cubic inch container.  To do that, set these two fractions equal to each other:

To set this up you put the container volumes in each numerator, and the corresponding denominator is the amount of peanut butter each container holds.  In the first case that would be 16 oz., in the second case it's x.  Now just solve for x using basic algebra:

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