Chapter 6.3, Problem 5CYU

To determine

To determine the numbers which satisfy the given situation

Answer to Problem 5CYU

The two numbers are 6 and 18.

Explanation of Solution

Given:

The sum of the two numbers is 24.

And, 5 times of first number minus the second number is 12.

Calculation:

Let,

The two numbers be x and y.

The sum of the two numbers is 24, which means,

  $x+y=24$

And, 5 times of first number minus the second number is 12, which means,

  $5x-y=12$

Let the equation,

  $x+y=\mathrm{24.......}(i)$

  $5x-y=\mathrm{12.......}(ii)$

Now, add equation ( i ) and equation ( ii ),

  $\begin{array}{l}\Rightarrow (x+y)+(5x-y)=24+12\\ \Rightarrow x+y+5x-y=36\\ \Rightarrow 6x=36\\ \Rightarrow x=6\end{array}$

Now, substitute the value of x in equation ( i ),

  $\begin{array}{l}\Rightarrow 6+y=24\\ \Rightarrow y=18\end{array}$

Conclusion:

Therefore, the required numbers are 6 and 18