Book I, Problem 18.Find three numbers such that thesum of any pair exceeds the third by a given amount;say the given excesses are 20, 30, and 40. [Hint:Letthe sum of all three numbers be 2x. Add number (3)to both sides of the equation (1)C(2)D(3)C20 toget (3)Dx10. Obtain expressions for (1) and (2)similarly.

Step-by-step explanation:

Let the three numbers be represented by a, b, c. Apparently, we want ...

  a + b = c + 20

  a + c = b + 30

  b + c = a + 40

Adding these three equations gives ...

  2a +2b +2c = a + b + c + 90

Subtracting a+b+c, we have ...

  a + b + c = 90

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Now, we can subtract each original equation from this to find one of the variables:

  (a +b +c) -(a +b) = (90) -(c +20)

  2c = 70

  c = 35

  (a +b +c) -(a +c) = (90) -(b +30)

  2b = 60

  b = 30

  c = 90 -35 -30 = 25

The three numbers are 25, 30, 35.

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step-by-step explanation: