SOLUTION: Here is my question; i have tried multiple times to solve it and looked at other solutions. The ones digit of a number is 1 more than twice the tens digit. If the digits are re

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Here is my question; i have tried multiple times to solve it and looked at other solutions. The ones digit of a number is 1 more than twice the tens digit. If the digits are re      Log On


   

Question 915066: Here is my question; i have tried multiple times to solve it and looked at other solutions.
The ones digit of a number is 1 more than twice the tens digit. If the digits are reversed, the new number is less than 3 times the original number. What is the original number? Thank you in advance for your help, and hopefully it comes fast.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The number originally could be T*10+U, using U for the ones digit and T for the tens digit.

Translate the description.
U=1%2B2T

Next part of the description needs care.
For U%2A10%2BT, condition is that cross%28%28U%2A10%2BT%29=-3%2B%28T%2A10%2BU%29%29. (Go to NEW INFORMATION, below here.)

You have two linear equations in the unknown variables, U and T.
Simplify the second part of the description, and then you could substitute for U from the first part of the description.


A FEW STEPS ---(NO. Go to NEW INFORMATION...)
10U%2BT=10T%2BU-3
10U-U%2BT-10T=-3
9U-9T=-3
9T-9U=3
3T-3U=1
you should be able to finish solving U and T.


NEW INFORMATION:
"...the new number is 8 less than 3 times the original number."

Changes to second equation make it then, %28U%2A10%2BT%29=-8%2B3%28T%2A10%2BU%29.
Either way, I had misunderstood part of the description.

The steps to start for simplifying this equation are straightforward:
10U%2BT=-8%2B3%2A10%2AT%2B3U
10U%2BT=30T%2B3U-8
7U-29T=-8
29T-7U=8
-
and your other equation from first part of the description, U=1%2B2T.

highlight%28system%28U=1%2B2T%2C29T-7U=8%29%29
This system should be uncomplicated to solve.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Here is my question; i have tried multiple times to solve it and looked at other solutions.
The ones digit of a number is 1 more than twice the tens digit. If the digits are reversed, the new number is less than 3 times the original number. What is the original number? Thank you in advance for your help, and hopefully it comes fast.


If there is a NUMBER between "is" and "less" in the sentence:

"If the digits are reversed, the new number is less than 3 times the original number?" Then

you need to provide that number!



However, if what you described above is correct, and with T being the tens digit, and

U being the units digit, the following equation and inequality can be formed:

U = 2T + 1 ------- (i)

10U + T < 3(10T + U)____10U + T < 30T + 3U____10U - 3U + T - 30T < 0

7U - 29T < 0 ----- (ii)



Based on the above, original numbers can be:

highlight_green%2849%29 

highlight_green%2837%29

highlight_green%2825%29, or

highlight_green%2813%29

You can do the check!! 

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

If you need a complete and detailed solution, let me know!!



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