Grades 7-8 Video Solutions 2023-2023_7-8

Video Transcription

Question 29. Jake wrote six consecutive numbers onto six white pieces of paper, one number on each piece. He stuck these bits of paper onto the top and bottom of  three coins. Then he tossed these three coins three times. On the first toss, he saw the numbers 6, 7, and 8 as shown, and then colored them red. In the second  toss, the sum of the numbers he saw was 23, and on the third toss, the sum was 17. What was the sum of the numbers on the remaining three white pieces of  paper? Since we know that there are six numbers that are in consecutive order, and we know that 6, 7, and 8 are numbers in this, these are four possible number  sequences. Now, since we know that the sum of the numbers in the second toss was 23, we can cross out this first sequence, since these numbers could not add up to  23. And, since we know that on the third toss, our sum was 17, we know that this is impossible in the third and fourth sequence of numbers. So with this, we are  left with the sequence of 4, 5, 6, 7, 8, and 9. Now, since we've already marked 6, 7, and 8 as red, we simply need to add 4 plus 5 plus 9 to get our answer, which will be A, 18.

Video Summary

Jake wrote six consecutive numbers and placed them on three coins. After tossing the coins, the visible numbers 6, 7, and 8 were marked. Subsequent tosses revealed sums of 23 and 17. Based on the sequences possible, only the series 4, 5, 6, 7, 8, and 9 fits all conditions. Numbers 6, 7, and 8 were already marked, leaving 4, 5, and 9. The sum of these remaining numbers is 18.