Question

A picket fence has slats that are 5/12 foot wide separated by gaps, that are 7/12 foot wide.How long is a fence with 30 slats

Answer 1

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$\bold{Explanation:}$

Let's first imagine how this picket fence would look like:

X__X__X__X .... X__X__X__X

Each X would be the 5/12 foot wide slat, and each __ is a 7/12 foot wide gap.

It's given that there are 30 slats, so how many gaps are there? There are 29 gaps in total.

So, all we have to do is solve

(30 x 5/12) + (29 x 7/12) = 150/12 + 203/12 = 353/12 = 29 and 5/12 feet wide.

Or, the simpler equation would be:

[29 x (5/12 + 7/12)] + 5/12  = (29 x 1) + 5/12 = 29 and 5/12 feet wide

Here, we considered each slat and gap as "one unit" and multiplied that by 29. The additional 5/12 is the last slat at the end.

Hope this helps!