A board 39 feet long is cut into 2 parts such that the length of the larger piece is 3 feet more than twice the length of the smaller piece. Find...

Given:

Length of the board =
39 ft

Length of the larger piece is 3 more than twice the
smaller
piece.

Required:

Length of
both pieces.

Solution:

Let the
length of the smaller piece is L.

Then the length of the
larger piece is 2L+3

But we know that the length of both
pieces is 39 ft.

==> 39= L +
(2L+3)

==> 39 = L +2L +
3

==> 39 = 3L + 3

Now
we will solve for L.

==> 3L + 3 =
39

We will subtract 3 from both
sides:

==> 3L =
39-3

==> 3L= 36

Now we
will divide by 3.

==> L = 36/3 =
12

Then, the length of the small piece is L= 12 and the
length of the larger piece is 2L+3 = 2*12+3= 27

To check we
will add both pieces we get 12 + 27= 39

Then,
the length of the smaller piece is 12 ft, and the length of the larger piece is 27
ft.