SOLUTION: This is not from a book but I am having difficulties with this question. The difference of two numbers is 27. The second is 1 less than 3 times the first. What are the two n

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Question 93010: This is not from a book but I am having difficulties with this question.
The difference of two numbers is 27. The second is 1 less than 3 times the first. What are the two numbers?
Any explanation would be helpful. Thank you.
Found 2 solutions by jim_thompson5910, ankor@dixie-net.com:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x-y=27 "The difference of two numbers is 27"

y=3x-1 "The second is 1 less than 3 times the first"

x-%283x-1%29=27 Plug in y=3x-1

x-3x%2B1=27 Distribute


-2x%2B1=27 Combine the variable terms 1x and -3x on the left side to get -2x



-2x=27-1 Subtract 1 from both sides




-2+x=26 Combine like terms -1 and 27 on the right side to get 26





x=%2826%29%2F%28-2%29 Now divide both sides by -2 to isolate and solve for x


x=+-13 Reduce



So our answer is
x=+-13


Plug in x=+-13 to find y


y=3%28-13%29-1

y=-39-1

y=-40


So the two numbers are -13 and -40

=====================================

Check:

-13+--40=27 Plug in x=-13 and y=-40

27=27 works

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!

Just write what it says:
:
"The difference of two numbers is 27."
One number = x
the 2nd number = (x-27)
:
"The second is 1 less than 3 times the first.
x - 27 = 3x - 1
:
What are the two numbers?
x - 3x = -1 + 27
-2x = +26
x = 26/-2
x = -13
:
2nd number: -13 - 27 = -40
:
Check using the statement "The second is 1 less than 3 times the first."
-40 = 3(-13) - 1