SOLUTION: I have tried multiple times to solve this problem, but each time I get the wrong answer ( I've checked in the back of the book). Question: " The difference of two numbers is 67.

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Question 210519This question is from textbook Intermediate Algebra
: I have tried multiple times to solve this problem, but each time I get the wrong answer ( I've checked in the back of the book).
Question: " The difference of two numbers is 67. The larger number is three less than six times the smaller number. Find the numbers."
I tried solving it like this:
x-y=67
larger number=6y-3
(6y-3)-y=67
The answers in the back of the book says 14 and 81. I am so lost in how they found that answer. This question is from textbook Intermediate Algebra

Found 3 solutions by stanbon, Alan3354, checkley77:
Answer by stanbon(48558) About Me  (Show Source):
You can put this solution on YOUR website!
The difference of two numbers is 67. The larger number is three less than six times the smaller number. Find the numbers."
I tried solving it like this:
x-y=67
larger number=6y-3
(6y-3)-y=67
The answers in the back of the book says 14 and 81.
----------------------------------------------------------
Since x-y = 67, the "x" must be the larger number.
Equation:
x = 6y-3
-----------------------
Substitute that into x-y=67 to get:
6y-3 - y = 67
5y = 70
y = 14
-------
Substitute that and solve for "x":
x = 6*14 -3
x = 84-3
x = 81
=======================================
Cheers,
Stan H.





Answer by Alan3354(21605) About Me  (Show Source):
You can put this solution on YOUR website!
Question: " The difference of two numbers is 67. The larger number is three less than six times the smaller number. Find the numbers."
I tried solving it like this:
x-y=67
larger number=6y-3
(6y-3)-y=67
---------------
14 and 81 does work.
---------------
x = larger #
y = smaller #
------------
x-y = 67
x = 6y-3
Sub for x into the 1st eqn
(6y-3) - y = 67
5y = 70
y = 14
x = 81


Answer by checkley77(12569) About Me  (Show Source):
You can put this solution on YOUR website!
Y-X=67
Y=6X-3
6X-3-X=67
5X=67+3
5X=70
X=14 ANS
Y-14=67
Y=67+14
Y=81 ANS.
PROOF:
81=6*14-3
81=84-3
81=81