There were 3 ribbons on the table. Ribbon A was the longest while Ribbon C
was the shortest. Ribbon B was twice as long as the shortest ribbon. The longest
ribbon was 6 times as long as the shortest ribbon. The total length of the three
ribbons was 4.68 m. What was the length of Ribbon A?

Let's break down the problem step by step.

Let the length of Ribbon C, the shortest ribbon, be \( x \) meters.

From the problem:
- Ribbon B is twice as long as Ribbon C, so the length of Ribbon B is \( 2x \) meters.
- Ribbon A is the longest and is 6 times as long as Ribbon C, so the length of Ribbon A is \( 6x \) meters.

The total length of the three ribbons is given as 4.68 meters, so we can set up the following equation:

\[
x + 2x + 6x = 4.68
\]

Simplifying the equation:

\[
9x = 4.68
\]

Now, solving for \( x \):

\[
x = \frac{4.68}{9} = 0.52 \, \text{meters}
\]

Thus, Ribbon C is 0.52 meters long.

Now, the length of Ribbon A, which is 6 times the length of Ribbon C, is:

\[
6x = 6 \times 0.52 = 3.12 \, \text{meters}
\]

So, the length of Ribbon A is **3.12 meters**.

Do you want more details on this process, or do you have any questions?

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Here are 5 related questions to further expand your understanding:
1. How would the total length change if Ribbon A were 5 times as long as Ribbon C instead of 6?
2. What is the combined length of Ribbons B and C?
3. If the total length was increased to 6 meters, how would that affect the length of Ribbon A?
4. What percentage of the total length is Ribbon B?
5. If Ribbon C were 0.6 meters, what would the length of Ribbon A be?

**Tip**: Whenever you solve word problems involving relationships between quantities, always translate the relationships into algebraic equations.

There were 3 ribbons on the table. Ribbon A was the longest while Ribbon C was the shortest. Ribbon B was twice as long as the shortest ribbon. The longest ribbon was 6 times as long as the shortest ribbon. The total length of the three ribbons was 4.68 m. What was the length of Ribbon A?

Solve the ribbon length problem using algebra. The total length of the ribbons is 4.68 meters, with Ribbon A being 6 times longer than Ribbon C. Learn how to find the length of Ribbon A using a simple linear equation. This problem is ideal for students in Grades 6-8.

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