A 12ft. board is cut into two pieces so that one piece is 8 ft. longer than 3 times the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces

x feet = short piece.

12-x = long piece.
3x+8 = 12-x
Solve for x.

x + (8 + 3x) = 12

4x + 8 = 12
4x + 8 - 8 = 12 - 8
4x = 4
x = 1

One piece is 1 foot long
The other piece is 11 feet long

Does that make sense?

(3 * 1) + 8 = 11

Let's assume that the length of the shorter piece is x feet.

According to the given information, the longer piece is 8 ft. longer than 3 times the shorter piece. Therefore, the length of the longer piece can be represented as (3x + 8) feet.

We know that the total length of the board is 12 ft. So, the sum of the lengths of the two pieces should be equal to 12 ft.

Therefore, we can write the equation:

x + (3x + 8) = 12

Simplifying the equation:

4x + 8 = 12

Subtracting 8 from both sides:

4x = 4

Dividing both sides by 4:

x = 1

So, the length of the shorter piece is 1 ft.

Substituting the value of x in the equation for the length of the longer piece:

3(1) + 8 = 3 + 8 = 11

Therefore, the length of the longer piece is 11 ft.

To find the lengths of both pieces, we can set up an equation based on the given information.

Let's assume that the shorter piece is x feet long. According to the problem, the longer piece is 8 feet longer than 3 times the shorter piece.

So, the length of the longer piece can be expressed as (3x + 8).

We also know that the total length of the board is 12 feet. Therefore, we can write the equation as:

x + (3x + 8) = 12

Simplifying the equation, we combine like terms:

4x + 8 = 12

Next, we isolate the variable by subtracting 8 from both sides:

4x = 4

Finally, we divide both sides by 4 to solve for x:

x = 1

Hence, the shorter piece is 1 foot long. To find the length of the longer piece, we substitute this value back into the expression (3x + 8):

Length of longer piece = (3 * 1) + 8 = 3 + 8 = 11 feet

Therefore, the lengths of the two pieces are 1 foot and 11 feet, respectively.