Question 670937: a 8 ft board is to be cut into three pieces, two equal length ones and the third 3 in shorter than the other two. If the cutting does not result in any length being lost, how long are the pieces?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the 3d length has to be less than the other 2.
this means that the maximum length of the 3d piece has to less than 8/3 feet.
if we're assuming that there has to be something left over, then the minimum length of the 3d piece has to be greater than 0.
so we have a minimum length of the 3d piece of greater than 0 and a maximum length of the 3d piece of smaller than 8/3.
anything in between should be ok.
example:
let the 3d piece be equal to 1 foot.
this means the 2 other pieces are 7/2 feet each.
let the 3d piece be equal to 2 feet.
this means the 2 other pieces at 6/2 feet each.
as long as you don't need to have integers, there are an infinite number of lengths that would satisfy the requirements.
if you assume some discrete amount, like no length could have an measurement that doesn't end in an inch, then you now have a finite number of possible solutions.
in fact, this probably means that the 3d piece needs to be in 2 inch increments which will allow the 2 equal pieces to be in 1 inch increments.
example:
3d piece equals 1 foot which means the 2 equal pieces equal 7/2 = 3.5 feet each.
3.5 is equivalent to 3 and 6 inches which is in increments of an inch so we're good.
if we increase 3d section to 1foot 1 inch then we have 6 feet 11 inches left which we divide by 2 to get 3 feet 5.5 inches which is less than inch increments so we're not good.
we would need to increase 3d section to 1 foot 2 inches (increments of 2 inches) to get 1 inch increments on the equal segments.
1 foot 2 inches from 8 feet leaves 6 feet 10 inches which divided by 2 equals 3 feet 5 inches for each of the equal segments.
not exactly sure what you were looking for but this is the solution based on my understanding of what you are asking.
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