Grades 9-10 Video Solutions 2023-2023_9-10

Video Transcription

A wooden fence consists of a series of vertical planks, each joined to the next post by four horizontal planks. The first and last plank in the fence are vertical.  Which of the following could be the total number of planks in the fence? Let's call the number of vertical planks that we have in our fence x.  Because there is exactly x vertical planks, there are x-1 gaps between these vertical planks, and the problem tells us that each of these gaps will be filled by four horizontal  planks. Therefore, in total, we use 4x-1 horizontal planks, and we have 4x-1 plus x, which is 5x-4 planks that are used overall.  Then we're searching for one of the answers to be in the form 5x-4. That is, we're looking for a number that's 4 less than a multiple of 5.  Clearly, 95 is a multiple of 5, 97 is 3 less than a multiple of 5, 98 is 2 less, and 99 is 1 less. So the only answer that satisfies the form we want is B, 96.

Video Summary

The problem involves calculating the total number of planks in a wooden fence comprised of vertical and horizontal planks, where the vertical planks number 'x'. The fence structure results in 'x - 1' horizontal gaps, each filled by four planks, leading to a total plank count of \(5x - 4\). The problem asks for a number fitting this format, specifically one that's 4 less than a multiple of 5. Among the given options, only 96 suits this form, as it can be expressed as \(5 \times 20 - 4\). Hence, the correct answer is 96.

Keywords

wooden fence

plank calculation

vertical planks

horizontal gaps

total plank count