College

The total length of two ribbons is 127.8 centimeters. The length of Ribbon A is 5 times the length of Ribbon B. What is the length of Ribbon A?

Answer :

To find the length of Ribbon A, we can follow these steps:

1. Define the variables:
- Let the length of Ribbon B be [tex]\( x \)[/tex] centimeters.

2. Express the length of Ribbon A in terms of Ribbon B:
- Since the length of Ribbon A is 5 times the length of Ribbon B, we can write:
[tex]\[
\text{Length of Ribbon A} = 5x
\][/tex]

3. Set up the equation based on the total length:
- According to the problem, the total length of the two ribbons is 127.8 centimeters. So, we can write the equation:
[tex]\[
x + 5x = 127.8
\][/tex]

4. Combine like terms:
- Simplify the equation:
[tex]\[
6x = 127.8
\][/tex]

5. Solve for [tex]\( x \)[/tex]:
- To find [tex]\( x \)[/tex], divide both sides of the equation by 6:
[tex]\[
x = \frac{127.8}{6} = 21.3
\][/tex]

6. Calculate the length of Ribbon A:
- Since Ribbon A is 5 times the length of Ribbon B:
[tex]\[
\text{Length of Ribbon A} = 5 \times 21.3 = 106.5 \text{ centimeters}
\][/tex]

So, the length of Ribbon A is [tex]\( 106.5 \)[/tex] centimeters.

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