Hardest Digit Problem Ever!!!!!?

Question

The units digit of a two-digit number is one-third the tens digit. When the digits are reversed, the new number is two more than four times the tens digit.Find the original number.


(Please help me solve this problem. I don't really know what does this means...Please also give me a solution...Thank you very much! God Bless!)

Please use only one variable and that variable is x

Answer 1

Let the unit digit be x. then 10s digit = 3x

the number = 10*3x + x = 31 x
when the digits are reversed the number = 10 x+3 x(tens digit becomes x and unit digit 3x so number ) = 13 x

from the given condition

13x = 12x+2

x = 2
so number = 62

Answer 2

I have no idea how much algebra you know, so here it is as simply as possible......

An example of a two digit number is 43, where '4' is the tens digit and '3' is the units digit. For the pupose of this question, we could say that 43 = 4x10 + 3. The why of this should be obvious soon.....

To solve this little problem, lets give the tens digit the value of 3 times n. This makes the units digit 'n'. Now the new number becomes, when the digits are reversed,

10n + 3n ( this is 10 times n plus three times n) which is thirteen times n.

We are told that if we multiply the original tens digit (3n) by 4 and add 2 we get 13 times n so now lets do some simple algebra...

from this statement (above) we have
13n = 12n + 2

Without using any crafty smoke and mirrors (magic) we can say "here we have 13 of this number equal to 12 of the number plus two, that being the case, the number must be two"

So lets test the answer (always a good idea)

The original number is 62,
reverse the digits, 26.
Multiply 6 by 4 and add 2 :- 6 x 4 = 24, add 2 gives 26
Eureka!

Answer 3

The unit digit has to be one-third of tens, so the tens can only be 9, 6 or 3, and hence the original number can be 93, 62 or 31. The original number is 62, since once you reverse the digits, i.e., 26 it is equal to 4 times tens, i.e., 4 times 6 plus 2 = 26.

Answer 4

Look first the ten digit. It must be divisible by 3. So there remains 3 possibilities 93 , 62 , 31
If you reverse the digits you obtain 39 , 26 , 13 . If you substract 2 the number must be divisible by 4. meets that prupose
Only 26 26 = 6*4 +2

The number was 62

Answer 5

Towards the end of your question, I think
you must mean "the tens digit of the original
number, otherwise it doesn't work out.
So that's what I will assume.

Let AB = the 2-digit number.
Then we know from the question, that :
B = A / 3, or A = 3B.

When you reverse the digits, you get BA.
This number in proper form = 10B + A.
Then we know from the question, that :
10B + A = 2 + 4A

But we found before, that A = 3B,
so substituting 3B wherever we find A, gives :
10B + 3B = 2 + 4(3B)

Adding like terms gives :
13B = 2 + 12B

Subtracting 12B from both sides gives :
B = 2

Substituting this into A = 3B gives :
A = 3(2) = 6

Therefore, the original number is 62.

Answer 6

10x + y = your number

"The units digit of a two-digit number is one-third the tens digit"
therefore: x = 3y (1)

"When the digits are reversed (10y + x), the new number is two more than four times the tens digit"
therefore: 10y + x = 4x + 2 --> 10y = 3x + 2 (2)

Substituting (1) into (2)
10y = 9y + 2
y = 2

x = 3y
x = 6

your number is 62

Answer 7

62

Answer 8

From the first clue, there are only three possible answers: 31, 62, and 93.

I believe 62 is the one you want.

Out of curiosity, where are you getting these problems? Why do you need the answers?

Answer 9

Could you please clarrify? "The new number is two more than four times the tens digit." The tens digit of the new reversed number or the original un-reversed number?