SOLUTION: Three numbers are in the ratio 3:9:10. If 10 is added to the last number, then the three numbers form an arithmetic progression. What are the three numbers?

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Question 1106490: Three numbers are in the ratio 3:9:10. If 10 is added to the last number, then the three numbers form an arithmetic progression. What are the three numbers?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) About Me  (Show Source):
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The numbers: 3x, 9x, 10x

Making the arithmetic progression: 3x, 9x, 10x+10

Common Difference between terms:
9x-3x=%2810x%2B10%29-9x
6x=10x%2B10-9x
6x=x%2B10
5x=10
highlight%28x=2%29

The three numbers (original numbers): 6, 18, 20

Answer by ikleyn(52788) About Me  (Show Source):
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.
The numbers are 3x, 9x and 10x for some x.


And the condition says that

3x, 9x and 10x + 10 

form an AP.  It implies


9x-3x = (10x+10) - 9x,   or


6x = x + 10  ====>  5x = 10  ====>  x = 2.


Answer.  The numbers are 6, 18  and 30.