Some decorations were lined up on both sides of a road for National Day coldbrel On one side of the road, the decoration has 5 lightbulbs for every 7m of wire on the other side, there were 5 stars for every 4m of wire The 2 wires used for the light bulbs and stars were of the same length There were 600 more stars than light bulbs along the entire stretch of road. What is the length of the road

Let the length of the road be denoted by \( L \) meters.

### Step 1: Expressions for the number of lightbulbs and stars
- On one side of the road, there are 5 lightbulbs for every 7 meters of wire. So, the total number of lightbulbs along that side is:
\[
\frac{5}{7}L
\]
- On the other side of the road, there are 5 stars for every 4 meters of wire. So, the total number of stars along that side is:
\[
\frac{5}{4}L
\]

### Step 2: Relating lightbulbs and stars
We are told that there are 600 more stars than lightbulbs, so we can set up the following equation:
\[
\frac{5}{4}L = \frac{5}{7}L + 600
\]

### Step 3: Solve the equation
First, eliminate the fractions by multiplying through by the least common denominator, which is 28:
\[
28 \times \frac{5}{4}L = 28 \times \frac{5}{7}L + 28 \times 600
\]
This simplifies to:
\[
35L = 20L + 16,800
\]

Now, subtract \( 20L \) from both sides:
\[
15L = 16,800
\]

Finally, solve for \( L \):
\[
L = \frac{16,800}{15} = 1,120 \, \text{meters}
\]

### Final Answer:
The length of the road is **1,120 meters**.

Would you like further details on the steps? Here are five related questions:

1. How would the problem change if the stars were 600 less than the lightbulbs?
2. What if both the lightbulbs and stars were placed on both sides of the road?
3. How would the equation change if the ratio of stars to meters was different?
4. Can you generalize this solution for any number of extra stars beyond 600?
5. How does this problem illustrate the concept of linear relationships in algebra?

**Tip**: Always try to eliminate fractions early in equations to make calculations easier.

Some decorations were lined up on both sides of a road for National Day coldbrel. On one side of the road, the decoration has 5 lightbulbs for every 7m of wire. On the other side, there were 5 stars for every 4m of wire. The 2 wires used for the light bulbs and stars were of the same length. There were 600 more stars than light bulbs along the entire stretch of road. What is the length of the road?

Learn how to solve a real-world algebraic problem involving the placement of lightbulbs and stars along a road. This example focuses on linear relationships and solving equations to find the length of the road, given there are 600 more stars than lightbulbs. Ideal for students in Grades 9-11.

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