Chapter 6.3, Problem 38HP

To determine

To write system of equations, solve and find the number.

Answer to Problem 38HP

26

Explanation of Solution

Given:

Sum of the digits of a two digit number: 8

Difference of the unit digit and the tens digit: -4

Calculation:

Let x represent the tens digit and y represent the units digit.

Sum of the units digit and the tens digit is 8.

  $\Rightarrow x+y=\mathrm{8.............}(1)$

Difference of the tens digit and the units digit is -4.

  $\Rightarrow x-y=-\mathrm{4..........}(2)$

Add equation (1) and equation (2),

  $\begin{array}{l}\Rightarrow (x+y)+(x-y)=8-4\\ \Rightarrow 2x=4\\ \Rightarrow x=\frac{4}{2}\\ \Rightarrow x=2\end{array}$

Substitute the value of x in equation (1)

  $\begin{array}{l}\Rightarrow 2+y=8\\ \Rightarrow y=8-2\\ \Rightarrow y=6\end{array}$

Therefore, the units digit is 6 and the tens digit is 2.

Conclusion:

Hence, the number is 26.