A 36 inch board is to be cut into three pieces so that the second piece is 3 times as long as the first piece and the third piece is 5 times as long as the first piece. If x represents the length of the first piece find the length s of all three pieces

x+3x+5x=36 inches

x=4inches

Well, let's turn this into a humorous mathematical puzzle, shall we?

Alright, so we have a 36-inch board and we need to cut it into three pieces. Let's call the length of the first piece "x."

Now, according to the problem, the second piece is 3 times as long as the first piece. So, if the first piece is x, the second piece would be 3x.

Moving on, the third piece is 5 times as long as the first piece. Therefore, the length of the third piece would be 5x.

Now, we need to add up the lengths of all three pieces and see if it equals the length of the board, which is 36 inches.

So, we have:

x + 3x + 5x = 36

Simplifying that expression, we get:

9x = 36

Now, let's find the value of x by dividing both sides of the equation by 9:

9x / 9 = 36 / 9

x = 4

So, the length of the first piece, x, is 4 inches!

Now, let's find the lengths of the second and third pieces.

The second piece, which is 3 times as long as the first piece (x), would be 3 * 4 = 12 inches.

The third piece, which is 5 times as long as the first piece (x), would be 5 * 4 = 20 inches.

Therefore, the lengths of the three pieces are:

First piece: 4 inches
Second piece: 12 inches
Third piece: 20 inches

And there you have it! The lengths of all three pieces of the board. I hope this math joke brought a smile to your face!

Let's solve this step by step.

Step 1: Define the variables
Let x be the length of the first piece.
Let y be the length of the second piece.
Let z be the length of the third piece.

Step 2: Set up the equation for the problem
According to the problem statement, the second piece is 3 times as long as the first piece, and the third piece is 5 times as long as the first piece.
So, we have the following equations:

y = 3x (second piece is 3 times the length of the first piece)
z = 5x (third piece is 5 times the length of the first piece)

Step 3: Set up the equation for the total length of the board
The total length of the board is 36 inches. So, the sum of the lengths of all three pieces should be equal to 36.
We can write this equation as:

x + y + z = 36

Step 4: Substitute the values of y and z from equations (1) and (2) into equation (3)

x + 3x + 5x = 36

Simplifying the equation:

9x = 36

Step 5: Solve for x

Divide both sides of the equation by 9:

x = 36 / 9
x = 4

So, the length of the first piece (x) is 4 inches.

Step 6: Substitute the value of x back into equations (1) and (2) to find the lengths of the second and third pieces.

y = 3x
y = 3(4)
y = 12

z = 5x
z = 5(4)
z = 20

Therefore, the lengths of the three pieces are as follows:
First piece (x) = 4 inches
Second piece (y) = 12 inches
Third piece (z) = 20 inches

To find the length of each piece, we can set up an equation based on the given information.

Let's represent the length of the first piece as x.

According to the problem, the second piece is 3 times as long as the first piece, so its length would be 3x.

Similarly, the third piece is stated to be 5 times as long as the first piece, making its length 5x.

The sum of the lengths of all three pieces should equal the length of the original board, which is 36 inches.

So we can write the equation: x + 3x + 5x = 36

Combining like terms on the left side, we have: 9x = 36

To isolate x, we divide both sides of the equation by 9: x = 36/9 = 4

Therefore, the length of the first piece (x) is 4 inches.

To find the lengths of the other two pieces, we substitute the value of x back into the expressions we derived earlier.

Second piece: 3x = 3 * 4 = 12 inches
Third piece: 5x = 5 * 4 = 20 inches

Therefore, the lengths of the three pieces are as follows:
First piece: 4 inches
Second piece: 12 inches
Third piece: 20 inches