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Two rational numbers that are not integers are added and also subtracted. The sum is 7 less than the difference. What could the numbers be?

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Answer:

  • one number is -3.5
  • the other number can be any non-integer rational, 3.4 for example

Explanation:

Let a and b represent the numbers, and let s and d represent the sum and difference.

a + b = s

a - b = d

We want ...

s = d -7

(a +b) = (a -b) -7

2b = -7 . . . . . . . . . add b-a to both sides

b = -7/2 . . . . the number subtracted to obtain the difference

There is nothing here that puts any restriction on the value of 'a'. The other number can be any value. We could have, for example, a = 3.4.

For a = 3.4, b = -3.5

sum = 3.4 +(-3.5) = -0.1

difference = 3.4 -(-3.5) = 6.9

The sum is 7 less than the difference:

6.9 -7 = -0.1 . . . as required

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