you have a piece of wood that is 144 inches long. you cut it into three pieces. the second piece is 12 inches longer than the first piece. the third piece is 12 inches longer than the second piece. write and solve the equation to find the lengths of the three pieces
36+48+60=144
To solve this problem, we need to define the lengths of the three pieces. Let's call the length of the first piece 'x' inches.
The second piece is stated to be 12 inches longer than the first piece, so its length can be expressed as 'x + 12' inches.
Similarly, the third piece is 12 inches longer than the second piece, so its length can be expressed as '(x + 12) + 12' inches, which simplifies to 'x + 24' inches.
Now, let's write an equation to represent the total length of the wood. We know that the total length is 144 inches, so we can set up the equation:
x + (x + 12) + (x + 24) = 144
Simplifying the equation, we combine like terms:
3x + 36 = 144
Next, we isolate the variable 'x' by subtracting 36 from both sides of the equation:
3x = 144 - 36
3x = 108
Finally, we solve for 'x' by dividing both sides of the equation by 3:
x = 108 / 3
x = 36
Thus, the first piece of wood is 36 inches long. Using this value, we can find the lengths of the other two pieces:
Second piece = x + 12 = 36 + 12 = 48 inches
Third piece = x + 24 = 36 + 24 = 60 inches
Therefore, the lengths of the three pieces are 36 inches, 48 inches, and 60 inches.