SOLUTION: The first 3 numbers exceeds the third by 1/2 of the second, the sum of second and third is one more than the first. if the second is subtracted from the sum of the first and third

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Question 1097069: The first 3 numbers exceeds the third by 1/2 of the second, the sum of second and third is one more than the first. if the second is subtracted from the sum of the first and third numbers the result is 5. Determined the numbers.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

Let the numbers be, in order, A, B, and C.

The first of 3 numbers exceeds the third by 1/2 of the second:
A+=+C+%2B+%281%2F2%29B (1)

The sum of second and third is one more than the first:
B%2BC+=+A%2B1 (2)

If the second is subtracted from the sum of the first and third numbers the result is 5:
A%2BC-B+=+5 (3)

The three equations we get by translating the given information directly are all in different forms; so it is not clear what might be the best way to solve the system. So I hope you get other answers from other tutors.... But this is the way I went:

Substituting (1) into (2) gives us

B%2BC+=+C+%2B+%281%2F2%29B+%2B+1
B+=+%281%2F2%29B%2B1
%281%2F2%29B+=+1
B+=+2

Substituting the value of B into (2) and (3) gives us

C%2B2+=+A%2B1 and C-2+=+-A%2B5

Adding those two equations gives us

2C+=+6
C+=+3

Then substituting the values of B and C into any of the original equations gives us A=4.

So the numbers are, in order, 4, 2, and 3.