algebra

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In the magic square shown (I'll type it out), the sum of the numbers in each row, column, and diagonal are the same. Five of these numbers are represented by v,w,x,y, and z. Find y + z.

Here's what the magic square looked like. I'll type semi-colons to separate each "square."

v; 24; w
18; x; y
25; z; 21

I don't know how to solve this at all. Considering that all of the other problems on this worksheet had to do with systems of 3 equations with 3 variables, I'm assuming I'll have to make a system of equations. How would I find this information in the magic square?

  • algebra -

    last row = second column
    25 + z + 21 = 24 + x + z
    x = 22

    second row = last row (we now know x=22)
    18+22+y = 25+z+21
    y = z + 6 #1

    first row = third colums
    v+24+w = w+y+21
    y=v+3 #2

    first row = right diagonal
    v+24+w = 25+x+w
    v+24 = 25+22
    v = 23

    then in #2 y = 23 + 3 = 26

    we now know the sum of each row from the second row:
    18+22+26 = 66

    so what do we have so far ?
    23 24 w
    18 22 26
    25 z 21

    from that w = 66-23-24 = 19
    z = 66-25-21 = 20

    check:
    23 24 19
    18 22 26
    25 20 21 OK!

  • algebra -

    There was really no method to what I did
    I noticed that the last row was a good one to use, since it contained only one variable

    from there it was just "hit or miss"
    there may very well be a better way.

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