Question

A farmer has decided to build a wire fence along one straight side of his property. He planned to place several fence posts at 6 m intervals, with posts fixed at both ends of the side. However, after buying the posts and wire, he found that the number of posts he had bought was 5 less than required. Later, he discovered that the number of posts he had bought would be just sufficient if he spaced them 8 m apart.

What is the length of the side of his property, and how many posts did he buy?

Options:

a) Length of the side: 168 m; Number of posts bought: 27
b) Length of the side: 172 m; Number of posts bought: 30
c) Length of the side: 176 m; Number of posts bought: 33
d) Length of the side: 180 m; Number of posts bought: 36

Answer 1

To find the length of the side of the farmer's property and the number of posts he bought, we can use algebraic equations to solve the problem step by step. The correct option is (Length of the side: 120 m; Number of posts bought: 14).

Step-by-step explanation:

To find the length of the side of the farmer's property and the number of posts he bought, let's solve this problem step by step.

1. Let's assume the required number of posts is 'n'.
2. If the posts are placed at 6 m intervals, the length of the side of the property will be (n+1)*6 m.
3. According to the problem, the number of posts the farmer bought is 5 less than required. So he bought (n-5) posts.
4. If these posts are spaced 8 m apart, the length of the side of the property will be [(n-5)+1]*8 m.
5. Equating the lengths of the property in both cases, we get (n+1)*6 = [(n-5)+1]*8.
6. Simplifying the equation, we have 6n + 6 = 8n - 32.
7. By solving this equation, we get n = 19.
8. Therefore, the length of the side of the property will be (19+1)*6 = 120 m, and the number of posts bought will be (19-5) = 14.

So, the correct option is (Length of the side: 120 m; Number of posts bought: 14).