A farmer has decided to build a wire fence along one straight side of his property. For this, he planned to place several fence-posts at 6 m intervals, with posts fixed at both ends of the side. After he bought the posts and wire, he found that the number of posts he had bought was 5 less than required. However, 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?
(a)100 m, 15
(b)100 m, 16
(c)120 m, 15
(d)120 m, 16
Answer
Answer (as printed): D
Explanation
Let the length of the side be $x$ metres. Then, number of posts required when placed 6 m apart $=\left(\frac{x}{6}+1\right)$. And, number of posts required when placed 8 m apart $=\left(\frac{x}{8}+1\right)$. $\therefore\left(\frac{x}{6}+1\right)-5=\left(\frac{x}{8}+1\right) \Leftrightarrow \frac{x}{6}-\frac{x}{8}=5 \Leftrightarrow \frac{x}{24}=5 \Leftrightarrow x=120 \mathrm{m}$. So, number of posts bought $=\left(\frac{120}{8}+1\right)=16$.