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6 October, 10:46

One number is 7 more than another. The difference between their squares is 161. What are their numbers?

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Answers (2)
  1. 6 October, 12:19
    0
    X-first number

    y-second number

    Assumption:

    x>y

    Equations:

    x=y+7

    x^2-y^2=161

    Put x from first equation to second:

    (y+7) ^2-y^2=161

    y^2+14y+49-y^2=161

    14y+49=161

    14y=161-49

    14y=112

    y=8, so x=y+7=15

    The solution is a pair of values: 8 and 15.
  2. 6 October, 14:10
    0
    Hello,

    Let's assume a the greatest number and b the smallest.

    a-b=7

    a²-b²=161==> (a-b) (a+b) = 161==>a+b=161/7==>a+b=23

    a+b=23

    a-b=7

    ==>2a=30==>a=15 and b=15-7=8

    Proof:

    15²-8²=225-64=161
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