# a board is 19 feet long and is cut in to two pieces one piece is 13 feet shorter then the other piece how long is the other piece?I know the obvious answer seems to be 6 but to me that seems to...

a board is 19 feet long and is cut in to two pieces one piece is 13 feet shorter then the other piece how long is the other piece?

I know the obvious answer seems to be 6 but to me that seems to easy. Is this the correct answer?

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You need to be very careful understanding the wording when doing word problems. This one does have some tricky wording.

When you are solving word problems like this, the first step is to write a "let statement." In this case, your let statement would be:

let x = longer piece (other piece)

let x -13 = shorter piece (given this info)

The second step is to write your equation:

19 = x + (x -13)

The third step is to solve for x:

19 = 2x - 13

32 = 2x

16 = x

The length of the other board is 16 ft and the shorter board given is 3 feet.

Let;

Length of the longer piece = x feet

Then:

Length of other piece = x - 13 feet

Therefore:

Length of two pieces = x + (x - 13) = 19 feet (given)

==> 2x - 13 = 19

==>2x = 19 + 13 = 32

==> x = 32/2 = 16

Therefore:

Length of longer piece = 16 feet

Length of the other piece = 16 - 13 = 3 feet

Total length = 19 feet.

Cut into two peoeces, one piece is 13 feet shorter than the other.

The procedure, without using algebra, is to keep 13 separate from 19. The rest is 19-13 = 6 which should be divided into two equals: 6/2 = 3 each. Then you get 3 and 3. Add 13 to one of the 3's. 2+13 = 16. So you are getting 3 and 16.

Now cut the 19 feet into 2 pieces 16 feet and 3 feet.

The pieces are 3 feet and 16 feet.

Tally:

Obviously 16 feet piece is 13 feet lager than 3 feet piece.. Two pieces put together 16 feet+3 feet = 19 feet.

Hope this helps.