Grades 5-6 Video Solutions 2021-video 2021 5-6/14

Video Transcription

14. The diagram shows three hexagons with numbers at their vertices, but some numbers are invisible. The sum of the six numbers around each hexagon is 30. What is the number  on the vertex marked with a question mark? What we can do is we can let A and B represent the two empty circles on the left hexagon,  and C and D represent the two empty circles on the right hexagon. Now we can use our givens that the sum of this is 30 to find out the values of these. So 3 plus 6 plus  1 plus 2 plus A plus B should be 30. So getting rid of all of these extra numbers, A plus B is equal to 18. On the right hand side, we have 4 plus 6 plus 9 plus 4 plus C plus  D is 30. So C plus D equals 7. Now let's take a look at the center hexagon. So the center hexagon is going to have question mark plus 1 plus A plus B plus C plus D equals  30. So thankfully we know all of C plus D and we know A plus B. So question mark plus 1 plus 7 plus 18 is 30. Question mark must be equal to 4. So the answer to this problem is B.

Video Summary

In the problem, there are three hexagons with numbers at the vertices. The sum of numbers around each hexagon is 30, but some numbers are missing. By assigning variables to missing numbers and using the known sums, equations are set up: \( A + B = 18 \) for the left hexagon and \( C + D = 7 \) for the right hexagon. In the center hexagon, where the unknown is marked with a question mark, the equation is \( ? + 1 + A + B + C + D = 30 \). Plugging in the known values gives \( ? + 1 + 18 + 7 = 30 \), resulting in the unknown number being 4.

Keywords

hexagons

vertex numbers

equations

sum

missing numbers