A log is 18 m long, correct to the nearest metre - OCR - GCSE Maths - Question 12 - 2017 - Paper 1

To facilitate calculations, we need to convert the length of the log from metres to centimetres. Since 1 m equals 100 cm, the length of the log in centimetres is:

$18.5 ext{ m} imes 100 = 1850 ext{ cm}$

The fence posts must be 80 cm long, but they are stated to be correct to the nearest 10 cm, meaning the actual length can range from 75 cm to 85 cm. For calculations, we will consider the maximum effective length of the posts as 85 cm.

To find the maximum number of fence posts that can be cut from the log, we divide the length of the log by the effective length of the posts:

$ext{Number of posts} = \left\lfloor \frac{1850 ext{ cm}}{80 ext{ cm}} \right\rfloor$

Calculating that gives:

$\frac{1850}{80} = 23.125$

Thus, the largest whole number of posts that can be cut from the log is 23.