# Question #9c419

Dec 3, 2016

58

#### Explanation:

Let in the two digit number the tens digit be x and units digit be y .
So the number is $\text{ } 10 x + y$

By the 1st condition

$\text{ } y - x = 3. \ldots \ldots \left(1\right)$

And by the2nd condition

$10 x + y - 4 \left(x + y\right) = 6$

$\implies 6 x - 3 y = 6$

$\implies 2 x - y = 2. \ldots . \left(2\right)$

Adding (1) and (2) we gwt

$x = 5$

Inserting $x = 5$ in (1) we get

$y - 5 = 3 \implies y = 8$

Hence the the two digit number is $10 x + y = 10 \times 5 + 8 = 58$

Dec 3, 2016

See explanation.

#### Explanation:

If we denote the tens digit by $a$ and unit digit by $b$ then the question leads to the following equations:

Tens digit is 3 less than units digit: $a = b - 3$.

The original number is six more than four times than the sum of dygits: $10 a + b - 6 = 4 \cdot \left(a + b\right)$.

If we solve the system we get:

$\left\{\begin{matrix}a = b - 3 \\ 10 a + b - 6 = 4 a + 4 b\end{matrix}\right.$

$\left\{\begin{matrix}a = b - 3 \\ 10 \left(b - 3\right) + b - 6 = 4 \left(b - 3\right) + 4 b\end{matrix}\right.$

Now from the second equation we calculate $b$:

$10 b - 30 + b - 6 = 4 b - 12 + 4 b$

$10 b + b - 8 b = 36 - 12$

$3 b = 24$

$b = 8$

So: $a = 8 - 3 = 5$