*Find the Number Satisfying the Given Conditions

[karush]

The sum of the digits of a two-digit number is $12$ The number is $13$ times the tens digit. Find the number

well from $3+9=12$ we can see that the number would be $39$ which is $3\times 13$

but again I had trouble knowing how to set this up

In that $10t+u=12$ how do you set up $13t=$

mahalo much...

 

[MarkFL]

I would let A be the ten's digit and B be the one's digit. We are then told:

(1) $\displaystyle A+B=12$

$\displaystyle 10A+B=13A$ or:

(2) $\displaystyle B=3A$

Now substitute for B into (1) using (2) to solve for A, then from (2) you will have B.

What number do you find?

 

[karush]

does it really have to be this easy...

A=3 then B=9

Oh and yes, Honolulu is a very nice place to live, me 12 years +

 

[MarkFL]

Yes, it is just that easy! (Handshake)

 

[CellCoree]

To find the number satisfying the given conditions, we can set up the following equations:

- The sum of the digits of a two-digit number is $12$: $t+u=12$, where $t$ is the tens digit and $u$ is the units digit.
- The number is $13$ times the tens digit: $10t+u=13t$, where $10t$ represents the tens digit and $u$ represents the units digit.

To solve for the number, we can substitute the first equation into the second equation:
$10t+u=13t$
$10(12-u)+u=13t$
$120-10u+u=13t$
$120-9u=13t$
$120=13t+9u$

Since we know that $t+u=12$, we can substitute $12$ for $t+u$ in the equation above:
$120=13t+9(12)$
$120=13t+108$
$12=13t$
$t=12/13$

Since $t$ is the tens digit, it must be a whole number. Therefore, $t=12/13$ is not a valid solution. This means that there is no two-digit number that satisfies the given conditions.