To solve this problem, we need to determine the lengths of two pieces of ribbon where one piece is three times as long as the other, given the total length of the ribbon is 272 cm.
Let's follow these steps to find the solution:
1. Define variables:
- Let [tex]\( x \)[/tex] be the length of the shorter piece.
- The length of the longer piece will then be [tex]\( 3x \)[/tex].
2. Set up an equation:
- The sum of the lengths of the two pieces equals the total length of the ribbon. Therefore, we write the equation:
[tex]\[
x + 3x = 272
\][/tex]
3. Combine like terms:
- Simplify the equation by combining the [tex]\( x \)[/tex] terms:
[tex]\[
4x = 272
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- To find the value of [tex]\( x \)[/tex], divide both sides of the equation by 4:
[tex]\[
x = \frac{272}{4}
\][/tex]
- Calculate the division:
[tex]\[
x = 68
\][/tex]
5. Find the length of the longer piece:
- The longer piece is three times the length of the shorter piece:
[tex]\[
3x = 3 \times 68
\][/tex]
- Perform the multiplication:
[tex]\[
3x = 204
\][/tex]
So, the length of the larger piece of the ribbon is 204 cm.
