SOLUTION: The sum of the digits of a two-digit number is 7. With the digits reversed the number is 5 times the tens digit of the original number. Find the original number. Thanks for the h

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Question 420199: The sum of the digits of a two-digit number is 7. With the digits reversed the number is 5 times the tens digit of the original number. Find the original number. Thanks for the help.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the digits of a two-digit number is 7.
With the digits reversed the number is 5 times the tens digit of the original number.
Find the original number.
:
Let x = the 10's digit
Let y = the units
then
10x + y = the original number
:
"The sum of the digits of a two-digit number is 7."
x + y = 7
x = (7-y); use this form for substitution
:
"With the digits reversed the number is 5 times the tens digit of the original"
10y + x = 5x
10y = 5x - x
10y = 4x
Substitute (7-y) for x
10y = 4(7-y)
10y = 28 - 4y
10y + 4y = 28
14y = 28
y = 28/14
y = 2
then
7 - 2 = 5 is x
:
52 is the original number