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

Video Transcription

A wire of length 95 meters is cut into three pieces such that the length of each piece is 50% more than the previous piece. What is the length of the largest piece?  Let's consider the longest length of wire after we make our two cuts. Let's call this length L. We know that each length is 50% more than the previous.  So that means that the next longest length must be 2 3rds L because 50% more than 2 3rds is 1.  Therefore we know that we have a length of L and then 2 3rds L. We can do the same thing again and going from 2 3rds L, 4 9ths L, 50% more than that would be 2 3rds.  So we have lengths of L, 2 3rds L, and 4 9ths L. Adding those three things up together, we get 19 L over 9 and we know that the total sum of these lengths is 95.  So solving for L, we find L equals 45 and therefore our answer is C, 45 meters.

Video Summary

The wire is cut into three pieces where each piece is 50% longer than the previous one. The longest piece is denoted as \( L \). Consequently, the next longest piece is \( \frac{2}{3}L \), and the shortest is \( \frac{4}{9}L \). Adding these gives \( \frac{19}{9}L \), which equals the total wire length of 95 meters. Solving for \( L \) gives the longest piece as 45 meters. Thus, the length of the largest piece is 45 meters.

Keywords

wire cutting

longest piece

proportional lengths

total wire length

solving equation