To determine the length of each piece of a 270-centimeter string divided in the ratio 2:3:4, let's break it down step-by-step:
1. Identify the given ratio and total length:
- The pieces are in the ratio 2:3:4.
- The total length of the string is 270 centimeters.
2. Express the lengths of each piece using a common variable [tex]\( x \)[/tex]:
- Let [tex]\( 2x \)[/tex] represent the length of the first piece.
- Let [tex]\( 3x \)[/tex] represent the length of the second piece.
- Let [tex]\( 4x \)[/tex] represent the length of the third piece.
3. Set up an equation based on the total length:
- The sum of the lengths of the pieces is equal to the total length of the string:
[tex]\[ 2x + 3x + 4x = 270 \][/tex]
4. Combine like terms:
- Combine the terms involving [tex]\( x \)[/tex]:
[tex]\[ 2x + 3x + 4x = 9x \][/tex]
- Thus, the equation becomes:
[tex]\[ 9x = 270 \][/tex]
5. Solve for [tex]\( x \)[/tex]:
- To find [tex]\( x \)[/tex], divide both sides of the equation by 9:
[tex]\[ x = \frac{270}{9} \][/tex]
[tex]\[ x = 30 \][/tex]
6. Calculate the length of each piece:
- The first piece, which is [tex]\( 2x \)[/tex]:
[tex]\[ 2x = 2 \times 30 = 60 \text{ centimeters} \][/tex]
- The second piece, which is [tex]\( 3x \)[/tex]:
[tex]\[ 3x = 3 \times 30 = 90 \text{ centimeters} \][/tex]
- The third piece, which is [tex]\( 4x \)[/tex]:
[tex]\[ 4x = 4 \times 30 = 120 \text{ centimeters} \][/tex]
So, the lengths of the three pieces are:
- First piece: 60 centimeters
- Second piece: 90 centimeters
- Third piece: 120 centimeters
