Grades 7-8 Video Solutions 2021-video 2021 7-8/10

Video Transcription

Question 10. Byron is 5 centimeters taller than Aaron but 10 centimeters shorter than Karen. Darren is 10 centimeters taller than Karen but 5  centimeters shorter than Aaron. Which of the following statements is true? I'll be using letters instead of the full names. So B or Byron is equal to Aaron's height  plus 5 centimeters since Byron is 5 centimeters taller than Aaron. We also know that Byron is 10 centimeters shorter than Karen so B equals C minus  10. Now since we know that Darren is 10 centimeters taller than Karen D equals C plus 10 but since Darren is 5 centimeters shorter than Aaron D equals  E minus 5. Now we know that Byron's height is greater than Aaron's height since Byron is taller. We also know that Karen is taller than Byron so C is  greater than B is greater than A. We know that Darren is 10 centimeters taller than Karen so D is greater than those and then we know that Darren is shorter  than Aaron so E is greater than D is greater than C is greater than B is greater than A. With this we can cross out the solutions A B and D since Aaron  is not taller than Aaron and they are also not equal in height. We just have to decide if Aaron is 10 centimeters or 30 centimeters shorter than Aaron. To do so  we just have to total up all of the heights since we know that Byron is 5 centimeters taller 10 centimeters shorter 10 centimeters taller and 5  centimeters shorter we do 5 plus 10 plus 10 plus 5 to get the difference between E and A. So our solution will be E. Aaron is 30 centimeters shorter than Aaron.

Video Summary

The problem involves comparing the heights of four individuals: Byron, Aaron, Karen, and Darren. Byron is 5 cm taller than Aaron and 10 cm shorter than Karen. Darren is 10 cm taller than Karen but 5 cm shorter than Aaron. Through a series of inequalities, it is established that Aaron is the tallest, followed by Darren, Karen, Byron, and Aaron in that order. The solution concludes that Aaron is 30 cm taller than Aaron, confirming who among them is the tallest by comparing all given height differences.