Grades 9-10 Video Solutions 2022-2022_9-10

Video Transcription

Question 14. Eva puts 2,022 tiles in a long line. Then, Adam removes every 6th tile. Next, Beata removes every 5th tile from those that remain. Then, Kale removes every 4th  tile. Finally, Doris removes all the remaining tiles. How many tiles does Doris remove? The first thing we should recognize is that 2,022 is divisible by 6. So to make this  problem more manageable, we can start off with a number of tiles that is smaller but also divisible by 6. So let's start with 12 tiles. We know that Adam removes every  6th tile, like so, Beata removes every 5th, and Kale removes every 4th. We can notice that we are left with 6 tiles, exactly half of the amount of tiles that we started with.  So if Doris removes all the remaining tiles, they are removing half of the original amount.  To find out how many Doris removed from the original 2,022 tiles, we simply have to divide this number by 2, and we get our answer, which is D, 1011.

Video Summary

In a problem-solving scenario, Eva begins with 2,022 tiles in a line. Adam removes every 6th tile, Beata every 5th from the remaining, and Kale every 4th from what's left after Beata. Finally, Doris removes all the remaining tiles. Observing a smaller case, beginning with 12 tiles and following the same removal sequence, half the tiles, six, remain for Doris to remove. Applying this pattern to the original 2,022 tiles, Doris removes half of them, resulting in 1,011 tiles being removed by Doris.

Keywords

problem-solving

tiles

removal sequence

pattern

Doris