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.

25 30 35

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.