Question

a community garden is surrounded by a fence. the total length of the fence is 3,000 ft. for every 48 ft of fence, there are 4 posts. what is the total number of posts in the fence? show your work.

Explanation:

Step1: Find posts per ft

First, find how many posts are there per foot of fence. Given 4 posts for 48 ft, so posts per ft is $\frac{4}{48}=\frac{1}{12}$ posts per ft.

Step2: Calculate total posts

The total length of the fence is 2000 ft. Multiply posts per ft by total length: $2000\times\frac{1}{12}=\frac{2000}{12}=\frac{500}{3}\approx166.67$? Wait, no, maybe I misread the total length. Wait, the image says "3000 ft"? Wait, the user's image: "The total length of the fence is 3000 ft" (maybe a typo in the text, let's check again. Wait, the user's text: "The total length of the fence is 3000 ft. For every 48 ft of fence, there are 4 posts. What is the total number of posts in the fence? Show your work." Oh, I see, I misread 3000. So let's correct.

Step1: Find posts per 48 ft ratio

For 48 ft, 4 posts. So the number of 48 - ft segments in 3000 ft: $\frac{3000}{48}$.

Step2: Multiply by posts per segment

Each segment has 4 posts, so total posts: $\frac{3000}{48}\times4$. Simplify $\frac{3000}{48}=\frac{3000\div12}{48\div12}=\frac{250}{4}=62.5$? No, wait, 3000 divided by 48: 4862 = 2976, 3000 - 2976 = 24, so 62.5? But posts must be whole? Wait, maybe the total length is 2000? Wait, no, the image: "The total length of the fence is 3000 ft" (assuming that). Wait, 48 ft has 4 posts, so posts per ft is 4/48 = 1/12. Then 3000 ft: 3000(1/12) = 250. Ah, yes, 3000 divided by 12 is 250. So correct steps:

Step1: Find posts per foot

Posts per foot = $\frac{4}{48}=\frac{1}{12}$ posts/ft.

Step2: Calculate total posts

Total length = 3000 ft. Total posts = $3000\times\frac{1}{12}=250$.

Answer:

250