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A fence is to be constructed with the following measurements:

Width between posts- 95"

Width of one slat- 3.5"

Spacing between slats- .5"

Calculate number of slats that will fit.

Thanks for your assistance.

There has to be one less space between the slats than the slats.

Just think about it - two slats, only one space between;

three slats, two spaces between; etc.

This means we need to find the greatest integer n such that

3.5n" + 0.5(n-1)" <= 95". This can be done since all of the measurements are in inches.

Omitting the inch measurement and multiplying it out gives 3.5n + 0.5n - 0.5 <= 95.

That reduces to 4n <= 95.5.

Dividing both sides by 4 gives n <= 23.875.

This means that we need n to be 23, since 24 would be to large.

The amount of field used would then be 4n- 0.5 where n=23, or 92-0.5 = 91.5".

This would leave 95" - 91.5" = 3.5" left over, which would be enough for another row,

but there is not enough for another 0.5" space in between.

Perhaps if I was doing it, I would add another row and only leave (11/23)" in between each row,

for that is only (1/46)" less than (1/2)".

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