Question

A 10 ft board is to be cut into three pieces, two equal- length ones and the third 9 in shorter than each of the other two. If the cutting does not result in any length being lost, how long are the pieces?

Answer 1

The two equal-length pieces are 43 inches each, and the third piece is 34 inches long.

Step-by-step explanation:

To solve this problem, we'll set up equations to represent the information given. Let's assume the length of the two equal-length pieces is 'x'. According to the problem, the third piece is 9 inches shorter than each of the other two. So the length of the third piece is 'x - 9'.

Since we have a total of 10 feet of board, which is equal to 120 inches, we can write the equation:

x + x + (x - 9) = 120

Simplifying the equation, we get:

3x - 9 = 120

Adding 9 to both sides, we have:

3x = 129

Dividing by 3, we find the value of x:

x = 43 inches

Therefore, the two equal-length pieces are 43 inches each, and the third piece is 34 inches long.

Answer 2

Let x represent one of the equal length sides making the third side which is 3 inches shorter than each of the other two equal to:

Third piece = x − 3 . Knowing that the whole board is 10 feet, in inches it is:

10 feet × 12 inches / 1 foot = 120 inches

To find the length of the pieces, add them and equate it to the legth of the board in inches as shown below:

x + x + x − 3 = 120 + 3

3 x /3 = 123 /3

x = 41 inches

Third piece = x − 3 =

41 − 3

= 38 inches

Step-by-step explanation: