Chapter 6.3, Problem 20PPS

To determine

To find the value of the two numbers.

Answer to Problem 20PPS

16, 25

Explanation of Solution

Given:

Sum of the numbers: 41

Difference of the numbers: 9

Calculation:

Let x and y be the two numbers

Given that the sum of the numbers is 41,

  $x+y=41\to (1)$

Also, the difference of the numbers is 9. Then,

  $x-y=9\to (2)$

Subtract (2) from (1),

  $\begin{array}{l}\Rightarrow (x+y)-(x-y)=41-9\\ \Rightarrow x+y-x+y=32\\ \Rightarrow 2y=32\\ \Rightarrow y=16\end{array}$

Substitute the value of $y=16$ in equation (2),

  $\begin{array}{c}x-16=9\text{ [Adding 16 on both sides] }\\ x=9+16\\ x=25\end{array}$

Conclusion:

Therefore, the numbers are 16 and 25.