Math Help?

In the magic square below, 5 more numbers can be placed so that the sum of the three numbers in any row, column, or diagonal will be the same. What value should X have?

15      A     35

50      B     C

25      X     D

2 Answers

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  • 2 months ago
    Favourite answer

    If you look at the first column, you have a sum of 90, so all the others must have the same sum of 90.

    Now look at the first row:

    15 + A + 35 = 90

    A + 50 = 90

    A = 40

    Then look at the diagonal going up to the right:

    25 + B + 35 = 90

    B + 60 = 90

    B = 30

    Finally look at the middle column:

    A + B + X = 90

    40 + 30 + X = 90

    X + 70 = 90

    X = 20

    Answer:

    X = 20 <--

    P.S. You could figure out C and D easily but it isn't necessary to find the value of X. If you did, the final square would be:

    15 40 35

    50 30 10

    25 20 45

    If you divide each number by 5 and subtract 1, you get a more typical magic square using the digits 1 to 9:

    2 7 6

    9 5 1

    4 3 8

  • RR
    Lv 6
    2 months ago

    15 + 50 + 25 = 90

    15 + 35 = 50, so A = 40

    25 + 35 = 60, so B = 30

    40 + 30 = 70, so X = 20

    check 

    25 + 20 = 45, so D = 45

    50 + 30 = 80, so C = 10

    35 + 10 + 45 = 90

    15 + 30 + 45 = 90

    Ans X = 20

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