Chapter 9.8, Problem 7P

To determine

To calculate:

The values of original numbers

Answer to Problem 7P

The values of original numbers are $2$ and $7$

Explanation of Solution

Given information:

Product of a two-digit number and its tens digit: $285$

Calculation:

Consider,

Tens digit: $x$

Ones digit: $y$

Now, as per the given condition of the problem:

  $\left(10x+y\right)x=285$  ... (1)

The ones digit is two more than ten digit:

  $y=x+2$  ... (2)

Put the value of $y$ in eq. (1):

  $\begin{array}{l}\left(10x+x+2\right)x=285\\ 11x^2+2x=285\\ 11x^2+2x-285=0\\ \left(11x+57\right)\left(x-5\right)=0\\ x=5orx=\frac{-57}{11}\end{array}$

Here, the correct value of $x$ is $2$ as there is not mention that value is negative.

Now, find the value of $y$ :

  $y=x+2=5+2=7$

Therefore, original numbers are $\left(x,y\right)=\left(2,7\right)$