Grades 7-8 Video Solutions 2021-video 2021 7-8/14

Video Transcription

Question 14. Costa is building a new fence in his garden. He uses 25 planks of wood, each of which are 30 cm long. He arranges these planks so that each pair of two adjacent planks overlaps by the same amount.  The total length of Costa's new fence is 6.9 m. What is the length of the overlap within each pair of adjacent planks in cm?  The diagram shows us that the fence will begin and end with planks at the very top. So that means there will be 13 planks on top and 12 on bottom.  Now we want to know what the length of the overlap is.  If we look at the bottom planks, we see that we can remove the adjacent parts, and there will be two ends per bottom plank that has to be removed.  And since we know that there are 12 planks on the bottom, we will have to do 12 times 2, or 24. And we know that the total length of this fence is 6.9 m.  Since we know that each individual plank of wood is 30 cm long, and there are 25 planks of wood used, then the total length will be 25 times 30 minus the length of the overlaps, or minus 24 ends.  We can begin with multiplying 25 by 30, and we get 750 cm, which we can simplify into 7.5 m. 7.5 m is the total length of all of the planks.  So we can subtract that from both sides, and make both sides positive. And we know that 60 cm is equal to the total of all of the adjacent parts, the 24 ends.  So to get our solution, we simply have to do 60 divided by 24 to get the length of each overlap. With that, we get our answer, B, 2.5.

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