SOLUTION: The second of three numbers is 3 times the first. The third is 5 more than the second. If the second is decreased by twice the third. The result is 5. What are the three numbers?

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Question 576539: The second of three numbers is 3 times the first. The third is 5 more than the second. If the second is decreased by twice the third. The result is 5. What are the three numbers?
The greater of two numbers is 3 more than the smaller. If twice the smaller is added to the greater, the result is 30. What are the numbers?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Let the three number be a, b, c
:
The second of three numbers is 3 times the first.
b = 3a
:
The third is 5 more than the second.
c = b+5
:
If the second is decreased by twice the third, the result is 5.
b - 2c = 5
From the above we can replace c with (b+5)
b - 2(b+5) = 5
b - 2b + 10 = 5
-b = 5 - 10
-b = -5
b = 5
then
c = 5 + 5
c = 10
and
b = 3a
5 = 3a
a = 5%2F3
:
What are the three numbers?: 5%2F3, 5, 10
:
:
The greater of two numbers is 3 more than the smaller.
a = b+3
:
If twice the smaller is added to the greater, the result is 30.
a + 2b = 30
Replace a with (b+3)
(b+3) + 2b = 30
3b = 30 - 3
3b = 27
b = 27%2F3
b = 9
then
a = 9 + 3
a = 12
:
What are the numbers? 12 and 9