SOLUTION: The greatest of three numbers is 10 more than the smallest. The remaining number is twice the smallest number. The greatest number is 2 more than the sum of the other two numbers.

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Question 1092823: The greatest of three numbers is 10 more than the smallest. The remaining number is twice the smallest number. The greatest number is 2 more than the sum of the other two numbers. Find the numbers.
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the 3 numbers in order of greatest to smallest =
+a+, +b+, and +c+
------------------------------
(1) +a+=+c+%2B+10+
(2) +b+=+2c+
(3) +a+=+b+%2B+c+%2B+2+
---------------------------
There are 3 equationd and 3 unknowns,
so it's solvable
Plug (1) and (2) into (3)
(3) +c+%2B+10+=+2c+%2B+c+%2B+2+
(3) +10+=+2c+%2B+2+
(3) +2c+=+8+
(3) +c+=+4+
and
(2) +b+=+2%2A4+
(2) +b+=+8+
and
(1) +a+=+4+%2B+10+
(1) +a+=+14+
---------------------
a = 14
b = 8
c = 4

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

The greatest of three numbers is 10 more than the smallest. The remaining number is twice the smallest number. The greatest number is 2 more than the sum of the other two numbers. Find the numbers.
Let the smallest number be S

Then largest = S + 10

Middle/2nd smallest/2nd largest = 2S

Also, S + 10 = S + 2S + 2

S + 10 = 3S + 2

S - 3S = 2 - 10

- 2S = - 8

S, or smallest number = highlight_green%28matrix%281%2C3%2C+%28-+8%29%2F%28-+2%29%2C+%22=%22%2C+4%29%29

You should be able to fund the other 2. I can't do everything for you.