Nonzero digits HELP Due tommorrow !! will give 10 points to answerer?

1. Given nonzero digits a, b, c such that number abc is divisible by 3, list some other numbers in terms of a, b, and ,c that are divisible by 3.

Please explain and show work.

2. Joan has the same number of sisters as she has brothers, but her brothers Matt has twice as many sisters as he has brothers. If there family has fewer than 10 childrens, how many of them are boys and how many are girls?

1 Answer

  • 1 decade ago
    Favorite Answer

    Number 1 does not make sense. However, ALL numbers divisible by 3 have something in common. If you add all the digits, the resulting number will be divisible by 3. EG: 75 = 7+5 = 12 = 1+2 = 3 So pick any digits, like 75, and add another valid number like 6, and you have that 567, 675, 765 and 576 are all divisble by 9. The same thing is true for 9. The sum of all digits of a number divisible by 9 will also always give you 9.

    And Joan's family can be expressed as Girls = X and boys = Y

    A: X-1 = Y

    (Girls minus Joan = number of boys)

    And B: Y-1 = X/2

    Boys minus matt = half the number of boys

    In equation B you can add 1 to get Y = X/2 +1

    So you can combine A and B to get X/2 +1 = X-1

    Multiply everything by 2:

    X+2 = 2X-2

    Get all your Xs on the same side

    X-2X+2 = -2

    Remove + from the left side

    X-2X = -4

    Resove the equation -X = -4 and X = 4. So there are 4 girls.

    X-1 = Y so 4-1 = Y 3=Y there are 3 boys.

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