a drinking straw of length 21 cm is cut into 3 pieces. the first length is x cm. the second piece is 3 cm shorter than the first piece. the third piece is twice as long as the first piece. state in terms of x the length of each of the pieces.
x + (x-3) +2x = 21
4x = 24
Solve for x and then compute the length of the other two peces from the information you have already been given.
21
To solve this problem, let's break it down step by step:
Step 1: Define the variables
Let's define the variables:
- x: length of the first piece
- second piece: 3 centimeters shorter than the first piece
- third piece: twice as long as the first piece
Step 2: Create the equations
We need to create equations based on the given information:
- The first piece: x centimeters
- The second piece: x - 3 centimeters (3 centimeters shorter than the first piece)
- The third piece: 2x centimeters (twice as long as the first piece)
Step 3: Combine the equations
According to the information given, the sum of the lengths of the three pieces should be equal to the length of the drinking straw, which is 21 centimeters. Therefore:
x + (x - 3) + 2x = 21
Step 4: Solve the equation
Combine like terms:
4x - 3 = 21
Add 3 to both sides of the equation:
4x = 24
Divide both sides of the equation by 4:
x = 6
Step 5: Determine the lengths of each piece
Now that we have found the value of x, we can substitute it back into the equations to find the lengths of each piece:
- The first piece: x = 6 centimeters
- The second piece: x - 3 = 6 - 3 = 3 centimeters
- The third piece: 2x = 2(6) = 12 centimeters
Therefore, the length of each piece is:
- The first piece: 6 centimeters
- The second piece: 3 centimeters
- The third piece: 12 centimeters