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

Video Transcription

Question 10. Avita wants to write the numbers 1 to 8 in the boxes of the grid shown, so that the sums of the numbers in the boxes in each row are equal,  and the sums of the numbers in the boxes of each column are equal. She has already written numbers 3, 4, and 8 as shown. What number will she write in the shaded box?  If we draw out our grid, we can write out letters A, B, C, D, and E to replace the unknown numbers for now. Now, we know that we will be using numbers 1 to 8,  so first let us take the sum of all these numbers, which will be 36. Now, to find out what value each sum of the column has to be, we can divide by 4, since there are 4 columns.  We get the number 9, so we know that each column is going to equal 9. So with the numbers that we already have, we know that 3 plus 6 will give us 9.  So we can replace A with 6, replace D with 5, and we can replace B with 1. Now, we are left with the numbers 2 and 7, but not if they should be an E or C.  To do this, we also have to recognize that the rows are equal, so we can set up an equation like so. 6 plus 4 plus 1 plus C is equal to 3 plus 5 plus 8 plus E.  Condensing these numbers together, we get 11 plus C is equal to 16 plus E. Now, since we have the numbers 2 and 7, we can replace C with 7 and E with 2,  so we'll make both sides equal to 18. Now we know that the shaded box will have the number 7, which is answer E.

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